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8 Gubkina St. Moscow,
119991, Russia
Tel.: +7(495) 984 81 41
Fax: +7(495) 984 81 39
Web site: www.mi-ras.ru
E-mail: steklov@mi-ras.ru

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Department of Number Theory

| Seminars | History of the Department | Research Directions | Main results | Publications |
Konyagin Sergei Vladimirovich

Doctor Phys.-Math. Sci., Professor, Academician of RAS, Head of Department, Chief Scientific Researcher
office: 520; tel.: +7 (495) 984 81 41 * 36-65; e-mail: konyagin23@gmail.com, konyagin@mi-ras.ru
Principal fields of research: Trigonometric series. Polynomials. Best approximation. Character sums.
Konyagin Sergei Vladimirovich
Balkanova Olga Germanovna

PhD, Scientific Researcher
office: 509; tel.: +7 (495) 984 81 41 * 36 07; e-mail: balkanova@mi-ras.ru
Principal fields of research: Analytic number theory, L-functions.
Balkanova Olga Germanovna
Frolenkov Dmitrii Andreevich

Candidate Phys.-Math. Sci., Senior Scientific Researcher
office: 509; tel.: +7 (495) 984 81 41 * 36 07; e-mail: frolenkov@mi-ras.ru
Principal fields of research: Analytic number theory. Automorphic functions. Kloosterman sums. $L$-functions. Continued fractions.
Frolenkov Dmitrii Andreevich
Gabdullin Mikhail Rashidovich

Candidate Phys.-Math. Sci., Scientific Researcher
office: 520; tel.: +7 (495) 984 81 41 * 36-65; e-mail: gabdullin@mi-ras.ru
Principal fields of research: analytic number theory, character sums, quadratic residues.
Gabdullin Mikhail Rashidovich
Korolev Maxim Aleksandrovich

Doctor Phys.-Math. Sci., Leading Scientific Researcher
office: 526; tel.: +7 (495) 984 81 41 * 37 32; e-mail: korolevma@mi-ras.ru
Principal fields of research: Incomplete Kloosterman sums, argument of Riemann's zeta-function, power residues, the average number of power residues, the problem of Lehmer–Landau.
Korolev Maxim Aleksandrovich
Radomskii Artyom Olegovich

Candidate Phys.-Math. Sci., Scientific Researcher
office: 210; e-mail: artyom.radomskii@mi-ras.ru
Rezvyakova Irina Sergeevna

Candidate Phys.-Math. Sci., Senior Scientific Researcher
office: 526; tel.: +7 (495) 984 81 41 * 37 32; e-mail: rezvyakova@mi-ras.ru
Principal fields of research: Analytic number theory.
Rezvyakova Irina Sergeevna
Shkredov Il'ya Dmitrievich

Doctor Phys.-Math. Sci., Corresponding Member of RAS, Chief Scientific Researcher
office: 509; tel.: +7 (495) 984 81 41 * 36 07; e-mail: ilya.shkredov@gmail.com, ishkredov@rambler.ru
Personal page: https://homepage.mi-ras.ru/~ishkredov/
Principal fields of research: Additive combinatorics, number theory, ergodic number theory.
Shkredov Il'ya Dmitrievich

Arkhipov Gennadii Ivanovich (12.12.1945 – 14.03.2013)

Doctor Phys.-Math. Sci.

Principal fields of research: Number theory, mathematical analysis.
Iskovskikh Vasilii Alekseevich (1.07.1939 – 4.01.2009)

Doctor Phys.-Math. Sci., Corresponding Member of RAS

Principal fields of research: Rationality problem, birational rigidity, birational classification.
Karatsuba Anatolii Alekseevich (31.01.1937 – 28.09.2008)

Doctor Phys.-Math. Sci.

Personal page: https://homepage.mi-ras.ru/~karatsuba
Principal fields of research: Analytic number theory and mathematical cybernetics.
Contemporary Problems in Number Theory
Seminar organizers: S. V. Konyagin; I. D. Shkredov; Seminar Secretary: D. Frolenkov
Steklov Mathematical Institute, Room 530 (8 Gubkina)
Number Theory irregular seminar
Seminar organizer: D. Frolenkov
Steklov Mathematical Institute, Gubkina, 8
History of the Department

The Department ofNumber Theory was organized in1934. Academician I.M.Vinogradov was the Head of the Department in 19341983. Since1983 Prof.A.A.Karatsuba is the Head of theDepartment.

In 2010 the Department of Number theory was merged with the Department of Algebra. Aleksei N. Parshin, corresponding member of the Russian Academy of Sciences, was appointed the head of the new Department of Algebra and Number theory. In 2016 the Department of Number theory has been re-established as as an independent unit of the institute. Head of the Department is S.V. Konyagin, corresponding member of the Russian Academy of Sciences.

At different times, G. I. Arkhipov, K.K.Mardzhanishvili, A.O.Gelfond, B.I.Segal, L.G.Shnirel'man, N.M.Korobov, L.P.Postnikova, N.V.Kuznetsov, S.A.Stepanov, A.I.Vinogradov, A.G.Postnikov, K.I.Oskolkov, S.M.Voronin, A.I.Pavlov, I.Yu.Fedorov, and M.E.Tchanga worked in the Department.

The most brilliant research achievements of the members of the Department include:

  • a new method of estimates of H.Weyl's sums and its applications in number theory;
  • an asymptotic formula for the number of representations of an odd integer by a sum of three prime numbers and, as corollary of this formula, the solution of the Goldbach problem;
  • the theory of trigonometric sums with prime numbers;
  • the solution of the 7th Hilbert problem on transcendency of logarithms of algebraic numbers;
  • rational approximations of linear forms of algebraic numbers and Diophantine equations;
  • the upper bound for the number of summands in the HilbertKamke problem;
  • elementary methods in additive problems with prime numbers;
  • the Waring problem and its generalizations to non-integer exponents;
  • the number theory methods in numerical analysis;
  • the large sieve and its applications.

Research Directions

Nowadays the number theory research is concentrated on additive combinatorics: the theory of sum products, estimates on the cardinality of sets having no solutions of linear equations; analytic number theory: distribution of prime numbers, the theory of the Riemann zeta function and its generalizations, Gram&39;s law, the theory of Dirichlet characters, incomplete Kloosterman sums, power residues, different additive problems, the theory of automorphic $L$-series, convolution formulas.

Main results

The members of the Department have made contribution to all main directions of analytic number theory as well as to some directions of applied mathematics, function theory, and algebraic geometry. In particular,

  • a local method of trigonometric sums was suggested which was used to construct a theory of multiple trigonometric sums similar to the classical Vinogradov's theory of Weyl's sums;
  • o problems about the exponent of convergence of singular integrals in the Tarry problem and its generalizations were solved;
  • the HilbertKamke problem and its generalizations to the multiple case were solved;
  • it was proved that strong forms of the Artin hypothesis on the number of variable forms or systems of forms, representing non-trivial zero in local fields are false;
  • a method of estimation of short sums of characters with modules equal to a power of a fixed prime number was discovered;
  • new elementary methods were developed in the theory of distribution of prime numbers and in the theory of equations over a finite field;
  • estimates of short sums of characters over shifted prime numbers in linear and non-linear case were obtained which are stronger than the results implied by the extended Riemann hypothesis;
  • the universality of the Riemann zeta-function and its generalizations was proved;
  • a new method of obtaining explicit formulae in additive problems of number theory was suggested;
  • a strong version of the Hilbert problem on differential independence of the Riemann zeta-function and its generalizations was proved;
  • the A. Selberg hypothesis on zeros of the Riemann zeta-function on short intervals of the critical line was proved;
  • a theorem about the `exclusiveness' of the critical line for zeros of the DavenportHeilbronn function and the Epstein zeta-function was proved;
  • on the basis of the Vinogradov method new properties of solutions of the Cauchy problem for Schroedinger type equations with periodic initial data were found and, in particular, a `quantum chaos' was discovered;
  • local and global properties of sums of trigonometric series with real algebraic polynomials in the index of imaginary exponent were studied;
  • algorithms of rapid multiplications of multi-digit numbers and of rapid calculation of elementary algebraic functions were found;
  • new quadrature formulae were constructed;
  • the three dimensional Luroth problem was solved;
  • a theory of rational surfaces over an algebraically non-closed field was developed and defining relations in the Cremona group of plane over an algebraically non-closed field were described;
  • the concept of birational rigidity, which is now one of the crucial concepts of higher dimensional birational geometry, was introduced and studied, a birational rigidity was proved for the main classes of higher dimensional Fano varieties and large classes of Fano fiber spaces.

Recent publications

| by years | scientific publications | by types |

1. S. Konyagin, H. Queffelec, E. Saksman, K. Seip, “Riesz projrctions and bounded mean oscjllation for Dirichlet series”, Studia Mathematica (to appear) , arXiv: 2005.11951v2
2. M. A. Korolev, “I.M.Vinogradovs sieve and the estimate of an incomplete Kloosterman sum”, Mat. Sb. (to appear)  mathnet
3. I. D. Shkredov, Uspekhi Mat. Nauk (to appear)  mathnet

4. S. Konyagin, P. Pollack, “A problem in comparative order theory”, Periodoca Mathematica Hungarica, 2022 (to appear) , arXiv: 2107.08998v2
5. M. A. Korolev, D. A. Popov, Izv. RAN. Ser. Mat. (to appear)  mathnet

6. K. Ford, S. Konyagin, “Divisibillity of the certain binomial coefficient $\binom{2n}{n}$”, Trans. Amer. Math. Soc., 374:2 (2021), 923–953 , arXiv: 1909.03903  mathnet  crossref  isi  scopus;
7. Analiticheskaya i kombinatornaya teoriya chisel, Sbornik statei. K 130-letiyu so dnya rozhdeniya akademika Ivana Matveevicha Vinogradova, Trudy MIAN, 314, ed. D. V. Treschev, S. V. Konyagin, V. N. Chubarikov, M. A. Korolev, M. R. Gabdullin, MIAN, M., 2021 , 346 pp.  mathnet
8. S. V. Konyagin, “On Irregularity of Finite Sequences”, Proc. Steklov Inst. Math., 314 (2021), 90–95  mathnet  crossref  crossref  isi  scopus
9. Kevin Ford, Sergey Konyagin, James Maynard, Carl B. Pomerance, Terence Tao, “Long gaps in sieved sets”, J. Eur. Math. Soc. (JEMS), 23:2 (2021), 667–700 , arXiv: 1802.07604  mathnet  crossref  isi  scopus;
10. P. A. Borodin, S. V. Konyagin, “Projection Greedy Algorithm”, Math. Notes, 110:1 (2021), 16–25  mathnet  crossref  crossref  isi
11. S. V, Konyagin, V. Yu. Protasov, “Ob odnoi lemme, voznikayuschei pri reshenii problemy Varinga”, Sibirskii matematicheskii zhurnal, 62:4 (2021), 803–806  mathnet  crossref
12. B. Kashin, S. Konyagin, V. Temlyakov, Sampling discretization of the uniform norm, 2021 , 34 pp., arXiv: 2104.01229v2
13. S. V. Konyagin, Min Sha, I. E. Shparlinski, C. L. Stewart, On the distribution of multiplicatively dependent vectors, 2021 , 25 pp., arXiv: 1903.09796v3
14. Kevin Ford, Sergey Konyagin, “Diffferences between totients”, Acta Arith., 200:1 (2021), 61–69 , arXiv: 2007.05771  mathnet  crossref  isi  scopus;
15. A. A. Karatsuba, “Five Lectures on the Life and Work of Academician I. M. Vinogradov”, Proc. Steklov Inst. Math., 314 (2021), 1–26  mathnet  crossref  crossref  isi  scopus
16. M. A. Korolev, “Kloosterman Sums with Primes and Solvability of a Congruence with Inverse Residues”, Proc. Steklov Inst. Math., 314 (2021), 96–126  mathnet  crossref  crossref  isi
17. A. T. Daniyarkhodzhaev, M. A. Korolev, “On a Ramanujan Identity and Its Generalizations”, Math. Notes, 110:4 (2021), 511–521  mathnet  crossref  crossref
18. I. D. Shkredov, “Modular hyperbolas and bilinear forms of Kloosterman sums”, J. Number Theory, 220 (2021), 182–211  mathnet  crossref  isi  scopus;
19. I. D. Shkredov, “On the Spectral Gap and the Diameter of Cayley Graphs”, Proc. Steklov Inst. Math., 314 (2021), 307–324  mathnet  crossref  crossref  isi  scopus
20. Olga Balkanova, Dmitry Frolenkov, “The second moment of symmetric square $L$-functions over Gaussian integers”, Proc. R. Soc. Edinb., Sect. A, Math., 2021, 1–27 (Published online) , arXiv: 2008.13399  mathnet  crossref  scopus; (Published online)
21. Olga Balkanova, Dmitry Frolenkov, “Non-vanishing of Maass form symmetric square $L$-functions”, J. Math. Anal. Appl., 500:2 (2021), 125148 , 23 pp.  mathnet  crossref  isi  scopus;
22. Olga Balkanova, Dmitry Frolenkov, “Moments of $L$-functions and the Liouville–Green method”, J. Eur. Math. Soc. (JEMS), 23:4 (2021), 1333–1380 , arXiv: 1610.03465  mathnet  crossref  isi  scopus;
23. Olga Balkanova, Dmitry Frolenkov, Morten S. Risager, “Prime geodesics and averages of the Zagier $L$-series”, Math. Proc. Camb. Philos. Soc., 2021, 1–24 (Published online)  mathnet  crossref  scopus; (Published online)
24. Artyom O. Radomskii, “Consecutive Primes in Short Intervals”, Proc. Steklov Inst. Math., 314 (2021), 144–202  mathnet  crossref  crossref  isi
25. Kevin Ford, Mikhail R. Gabdullin, “Sets whose differences avoid squares modulo $m$”, Proc. Amer. Math. Soc., 149 (2021), 3669–3682  mathnet  crossref  isi  scopus;
26. Olga Balkanova, “The first moment of Maass form symmetric square $L$-functions”, Ramanujan J., 55 (2021), 761–781  mathnet  crossref  isi (cited: 1)  scopus (cited: 1); (Published online)
27. Olga Balkanova, Bingrong Huang, Anders Södergren, “Non-vanishing of Maass form $L$-functions at the central point”, Proc. Amer. Math. Soc., 149:2 (2021), 509–523  mathnet  crossref  isi (cited: 1)  scopus (cited: 1); (Published online)

28. Sergei Konyagin, Benny Sudakov, “An extremal problem for integer sparse recovery”, Linear Algebra Appl., 56:1 (2020), 1–6 , arXiv: 1904.08661v2  mathnet  crossref  mathscinet  isi  scopus;
29. S. V. Konyagin, . E Shaparlinski, I. V. Vyugin, Polynomial equations in subgroups and applications, 2020 , 23 pp., arXiv: 2005.08315v1
30. Sergei V. Konyagin, Sergey V. Makarychev, Igor E. Shparlinski, Ilya V. Vyugin, “On the structure of graphs of Markoff triples”, Q. J. Math., 72:2 (2020), 637–648 , arXiv: 1711.05335  mathnet  crossref  mathscinet  isi  scopus;
31. S. V. Konyagin, “On Zeros of Sums of Cosines”, Math. Notes, 108:4 (2020), 538–541  mathnet  crossref  crossref  mathscinet  isi  elib  scopus
32. A. R. Alimov, A. A. Vasil'eva, S. V. Konyagin, A. S. Kochurov, A. I. Kozko, T. P. Lukashenko, K. S. Ryutin, V. M. Tikhomirov, A. V. Fursikov, V. N. Chubarikov, “Igor Germanovich Tsarkov (to 60th anniversary)”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2020, no. 4, 70–71  mathnet
33. S. V, Konyagin, A. Yu. Shadrin, “Ob ustoichivom vosstanovlenii analiticheskikh funktsii po vyborke iz koeffitsientov ryada Fure”, Trudy Instituta matematiki i mekhaniki UrO RAN, 26:4 (2020), 182–195  mathnet  crossref  isi  elib
34. V. V. Arestov, V. I. Berdyshev, M. V. Deikalova, S. V. Konyagin, D. S. Telyakovskii, “On the International Workshop-Conference on Function Theory Dedicated to the Centenary of the Birth of S.B. Stechkin”, Trudy Inst. Mat. i Mekh. UrO RAN, 26, no. 4, 2020, 290–299  mathnet  crossref  mathscinet  isi  elib
35. M. R. Gabdullin, S. V. Konyagin, “Stechkins works in number theory”, Chebyshevskii Sb., 21:4 (2020), 9–18  mathnet  crossref
36. M. A. Korolev, A. V. Shubin, “The second moment of the first derivative of Hardys $Z$-function”, Trigonometric Sums and Their Applications, eds. A. Raigorodskii, M. T. Rassias, Springer Nature Switzerland AG, 2020, 169–182  crossref  scopus
37. M. A. Korolev, M. E. Changa, “New Estimate for Kloosterman Sums with Primes”, Math. Notes, 108:1 (2020), 87–93  mathnet  crossref  crossref  mathscinet  isi (cited: 1)  elib  scopus (cited: 1)
38. Maxim A. Korolev, “Kloosterman sums over primes of composite moduli”, Res. Number Theory, 6 (2020), 24 , 20 pp.  mathnet  crossref  mathscinet  isi (cited: 1)  scopus;
39. M. A. Korolev, “Obmanchivaya prostota prostykh chisel”, Kvant, 2020, no. 3, 10–17  mathnet  crossref
40. Maxim Korolev, Igor Shparlinski, “Sums of algebraic trace functions twisted by arithmetic functions”, Pacific J. Math., 304:2 (2020), 505–522 , arXiv: 1804.01337  mathnet  crossref  mathscinet  zmath  adsnasa  isi (cited: 3)  scopus (cited: 3);
41. M. A. Korolev, “Kloosterman sums with primes and the solvability of one congruence with inverse residues — II”, Chebyshevskii sb., 21:1 (73) (2020), 200–211  mathnet (cited: 1)  crossref  crossref  mathscinet;
42. Maxim Korolev, Antanas Laurinčikas, “A new application of the Gram points. II”, Aequationes Math., 94 (2020), 1171–1187  mathnet  crossref  mathscinet  zmath  isi (cited: 2)  scopus (cited: 2);
43. V. M. Buchstaber, M. A. Korolev, “On the scientific works of Dmitry Alexandrovich Popov”, Chebyshevskii Sb., 21:4 (2020), 396–421  mathnet  crossref  crossref
44. I. D. Shkredov, “A remark on sets with small Wiener norm”, Trigonometric Sums and Their Applications, eds. Raigorodskii A., Rassias M. (eds), Springer, Cham, 2020, 261–272  crossref  scopus
45. I. D. Shkredov, “Any small multiplicative sugroup is not a sumset”, Finite Fields Appl., 63 (2020), 101645 , 15 pp.  mathnet  crossref  mathscinet  isi (cited: 1)  scopus (cited: 1);
46. M. Rudnev, G. Shakan, I. D. Shkredov, “Stronger sum-product inequalities for small sets”, Proc. Amer. Math. Soc., 148 (2020), 1467–1479  mathnet  crossref  mathscinet  isi (cited: 3)  scopus (cited: 10);
47. Misha Rudnev, Ilya D. Shkredov, Sophie Stevens, “On the energy variant of the sum-product conjecture”, Rev. Mat. Iberoam., 36:1 (2020), 207–232  mathnet  crossref  mathscinet  isi (cited: 5)  scopus (cited: 26);
48. T. Schoen, I. D. Shkredov, “$L$-functions and sum-free sets”, Acta Math. Hung., 161 (2020), 427–442  mathnet  crossref  mathscinet  isi  scopus;
49. K. I. Olmezov, A. S. Semchankau, I. D. Shkredov, “On Popular Sums and Differences for Sets with Small Multiplicative Doubling”, Math. Notes, 108:4 (2020), 557–565  mathnet  crossref  crossref  mathscinet  isi (cited: 1)  elib  scopus
50. Vsevolod F. Lev, Ilya D. Shkredov, “Small doubling in prime-order groups: from 2.4 to 2.6”, J. Number Theory, 217 (2020), 278–291  mathnet  crossref  mathscinet  isi (cited: 1);
51. Nikolay Moshchevitin, Brendan Murphy, Ilya Shkredov, “Popular products and continued fractions”, Israel J. Math., 238 (2020), 807–835  mathnet  crossref  mathscinet  isi (cited: 2)  scopus (cited: 2);
52. Simon Macourt, Giorgis Petridis, Ilya D. Shkredov, Igor E. Shparlinski, “Bounds of Trilinear and Trinomial Exponential Sums”, SIAM J. Discrete Math., 34:4 (2020), 2124–2136  mathnet  crossref  mathscinet  isi (cited: 1)  scopus (cited: 1);
53. N. G. Moshchevitin, I. D. Shkredov, “On a modular form of Zarembas conjecture”, Pacific J. of Math., 309:1 (2020), 195–211  mathnet  crossref  isi (cited: 1)  scopus (cited: 1)
54. O. Balkanova, G. Bhowmik, D. Frolenkov, N. Raulf, “Mixed moment of $GL(2)$ and $GL(3)$ $L$-functions”, Proc. London Math. Soc. (3), 121:2 (2020), 177–219 , arXiv: 1811.03553  mathnet  crossref  isi  scopus;
55. Dmitry Frolenkov, “The cubic moment of automorphic $L$-functions in the weight aspect”, J. Number Theory, 207:2 (2020), 247–281  mathnet  crossref  mathscinet  zmath  isi  scopus;
56. D. A. Frolenkov, “Nondiagonal terms in the second moment of automorphic $L$-functions”, Sb. Math., 211:8 (2020), 1171–1189  mathnet  crossref  crossref  mathscinet  isi  elib  scopus
57. Olga Balkanova, Dmitry Frolenkov, “Prime geodesic theorem for the Picard manifold”, Adv. Math., 375 (2020), 107377 , 42 pp., arXiv: 1804.00275  mathnet  crossref  mathscinet  isi (cited: 1)  scopus (cited: 2);
58. A. O. Radomskii, “Some trigonometric polynomials with extremely small uniform norm and their applications”, Izv. Math., 84:2 (2020), 361–391  mathnet  crossref  crossref  mathscinet  isi  elib  scopus
59. M. R. Gabdullin, “Lower Bounds for the Wiener Norm in $\mathbb Z_p^d$”, Math. Notes, 107:4 (2020), 574–588  mathnet  crossref  crossref  mathscinet  isi  elib  scopus
60. M. R. Gabdullin, Dokl. RAN. Math. Inf. Proc. upr., 491:1 (2020), 19–22  mathnet  crossref  isi  elib

61. M. A. Korolev, A. V. Ustinov, “Distribution of rational points on the circle of unit radius”, Izv. Math., 83:5 (2019), 1008–1049  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
62. M. A. Korolev, “Short Kloosterman Sums with Primes”, Math. Notes, 106:1 (2019), 89–97  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 3)  elib  scopus (cited: 3)
63. M. A. Korolev, Kloosterman sums with primes to composite moduli, 2019 , 23 pp., arXiv: 1911.09981  adsnasa
64. M. E. Changa, M. A. Korolev, Kloosterman sums with primes and the solvability of one congruence with inverse residues. I, 2019 , 38 pp., arXiv: 1911.12589  adsnasa
65. M. A. Korolev, “O razreshimosti v prostykh chislakh nekotorykh sravnenii s obratnymi velichinami”, Algebra, teoriya chisel i diskretnaya geometriya: sovremennye problemy, prilozheniya i problemy istorii: Materialy XVI Mezhdunarodnoi konferentsii, posvyaschennoi 80-letiyu so dnya rozhdeniya professora Mishelya Deza (Tula, 13-18 maya 2019 g.), Biblioteka Chebyshevskogo sbornika, eds. V. N. Chubarikov, N. M. Dobrovolskii, I. Yu. Rebrova,N. N. Dobrovolskii, Tul. gos. ped. un-t im. L.N. Tolstogo, 2019, 37–39
66. M. A. Korolev, “Ob odnom obschem svoistve ryadov Fareya”, Algebra, teoriya chisel i matematicheskoe modelirovanie dinamicheskikh sistem: Tezisy Mezhdunarodnoi konferentsii Algebra, teoriya chisel i matematicheskoe modelirovanie dinamicheskikh sistem, posvyaschennoi 70-letiyu A.Kh. Zhurtova (Nalchik, 29 iyunya - 3 iyulya 2019 g.), Nalchik: Izd-vo KBGU, 2019, 2019, 58–59 http://algebra.imm.uran.ru/conf-algebra/algebra/trudy2019.pdf
67. Alexandar P. Ivić, Maxim A. Korolev, “On the distribution of values of the argument of the Riemann zeta-function”, J. Number Theory, 200 (2019), 96–131 , arXiv: 1808.10768  mathnet  crossref  mathscinet  zmath  adsnasa  isi  scopus
68. Maxim Korolev, Antanas Laurinčikas, “A new application of the Gram points”, Aequationes Math., 93:5 (2019), 859–873  mathnet  crossref  mathscinet  zmath  isi (cited: 4)  scopus (cited: 4);
69. Ilya D. Shkredov, “Some remarks on the asymmetric sum–product phenomenon”, Moscow J. Combin. Number Theory, 8:1 (2019), 15–41  mathnet  crossref  mathscinet  zmath  scopus (cited: 7)
70. I. D. Shkredov, “A Short Remark on the Multiplicative Energy of the Spectrum”, Math. Notes, 105:3-4 (2019), 449–457  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  scopus
71. Oliver Roche-Newton, Ilya D. Shkredov, “If $A+A$ is small then $AAA$ is superquadratic”, J. Number Theory, 201 (2019), 124–134  mathnet  crossref  mathscinet  zmath  isi (cited: 2)  scopus (cited: 2)
72. Oliver Roche-Newton, Imre Z. Ruzsa, Chun-Yen Shen, Ilya D. Shkredov, “On the size of the set $AA+A$”, J. London Math. Soc., 99:2 (2019), 477–494  mathnet  crossref  mathscinet  zmath  isi (cited: 1)  scopus (cited: 1)
73. T. Schoen, I. D. Shkredov, “An upper bound for weak $B_k$–sets”, SIAM J. Discrete Math., 33:2 (2019), 837–844  mathnet  crossref  mathscinet  zmath  isi (cited: 1)  scopus (cited: 1)
74. Brendan Murphy, Giorgis Petridis, Oliver Roche-Newton, Misha Rudnev, Ilya D. Shkredov, “New results on sum-product type growth over fields”, Mathematika, 65:3 (2019), 588–642  mathnet  crossref  mathscinet  zmath  isi (cited: 9)  scopus (cited: 27)
75. Ilya D. Shkredov, “Some remarks on products of sets in the Heisenberg group and in the affine group”, Forum Math., 32:1 (2019), 189–200  mathnet  crossref  mathscinet  isi (cited: 2)  scopus (cited: 2);
76. Pierre-Yves Bienvenu, François Hennecart, Ilya Shkredov, “A note on the set $A(A+A)$”, Moscow J. Combin. Number Theory, 8:2 (2019), 179–188  mathnet  crossref  mathscinet  zmath  scopus (cited: 1);
77. B. Murphy, M. Rudnev, I. D. Shkredov, Yu. N. Shteinikov, “On the few products, many sums problem”, J. Théor. Nombres Bordx., 31:3 (2019), 573–602  mathnet  crossref  isi (cited: 3)  scopus (cited: 14);
78. Olga Balkanova, Dmitry Frolenkov, “Bounds for a spectral exponential sum”, J. London Math. Soc., 99:2 (2019), 249–272 , arXiv: 1803.04201  mathnet  crossref  mathscinet  zmath  isi (cited: 7)  scopus (cited: 8)
79. Olga Balkanova, Dimitrios Chatzakos, Giacomo Cherubini, Dmitry Frolenkov, Niko Laaksonen, “Prime geodesic theorem in the 3-dimensional hyperbolic space”, Trans. Amer. Math. Soc., 372:8 (2019), 5355–5374 , arXiv: 1712.00880  mathnet  crossref  mathscinet  zmath  isi (cited: 4)  scopus (cited: 6)
80. Olga Balkanova, Gautami Bhowmik, Dmitry Frolenkov, Nicole Raulf, “A mean value result for a product of $GL(2)$ and $GL(3)$ $L$-functions”, Mathematika, 65:3 (2019), 743–762 , arXiv: 1710.01388  mathnet  crossref  mathscinet  zmath  isi (cited: 1)  scopus (cited: 1)
81. Olga Balkanova, Dmitry Frolenkov, “Sums of Kloosterman sums in the prime geodesic theorem”, Q. J. Math., 70:2 (2019), 649–674 , arXiv: 1803.04206  mathnet  crossref  mathscinet  isi (cited: 3)  scopus (cited: 4)
82. Olga Balkanova, Dmitry Frolenkov, “Convolution formula for the sums of generalized Dirichlet L-functions”, Rev. Mat Iberoam, 35:7 (2019), 1973–1995 , arXiv: 1709.01365  mathnet  crossref  mathscinet  zmath  isi (cited: 2)  scopus (cited: 3)

83. K. Ford, B. Green, S. Konyagin, J. Maynard, T. Tao, “Long gaps between primes”, J. Amer. Math. Soc., 31:1 (2018), 65–105 , arXiv: 1412.5029  mathnet  crossref  mathscinet  zmath  isi (cited: 13)  elib  scopus (cited: 18)
84. S.V. Konyagin, I.D. Shkredov, “On subgraphs of random Cayley sum graphs”, European J. Combin., 70 (2018), 61–74 , arXiv: 1710.07230  mathnet  crossref  mathscinet  isi (cited: 1)  scopus (cited: 3)
85. S. V. Konyagin, A. A. Kuleshov, V. E. Maiorov, “Some Problems in the Theory of Ridge Functions”, Proc. Steklov Inst. Math., 301 (2018), 144–169  mathnet  crossref  crossref  mathscinet  isi (cited: 2)  elib  elib  scopus (cited: 2)
86. P. A. Borodin, S. V. Konyagin, “Convergence to zero of exponential sums with positive integer coefficients and approximation by sums of shifts of a single function on the line”, Anal. Math., 44:2 (2018), 163–183  mathnet  crossref  mathscinet  isi (cited: 7)  scopus (cited: 6)
87. S. V. Konyagin, “On the Recovery of an Integer Vector from Linear Measurements”, Math. Notes, 104:6 (2018), 859–865  mathnet  crossref  crossref  crossref  mathscinet  zmath  isi (cited: 3)  elib  elib  scopus (cited: 3)
88. M. A. Korolev, “New estimate for a Kloosterman sum with primes for a composite modulus”, Sb. Math., 209:5 (2018), 652–659  mathnet  crossref  crossref  mathscinet  adsnasa  isi (cited: 8)  elib  scopus (cited: 8)
89. M. A. Korolev, “Kloosterman sums with multiplicative coefficients”, Izv. Math., 82:4 (2018), 647–661  mathnet  crossref  crossref  mathscinet  adsnasa  isi (cited: 1)  elib  scopus (cited: 1)
90. M. A. Korolev, “Elementary Proof of an Estimate for Kloosterman Sums with Primes”, Math. Notes, 103:5 (2018), 761–768  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 2)  elib  scopus (cited: 3)
91. M. A. Korolev, “Divisors of a quadratic form with primes”, Proc. Steklov Inst. Math., 303 (2018), 154–170  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 3)  elib  scopus (cited: 2)
92. M. A. Korolev, A. V. Ustinov, “The Distribution of the Rational Points on the Unit Circle”, Dokl. Math., 98:1 (2018), 321–324  mathnet  crossref  crossref  zmath  isi  elib  elib  scopus
93. M. A. Korolev, I. E. Shparlinski, Sums of algebraic trace functions twisted by arithmetic functions, 2018 , 19 pp., arXiv: 1804.01337  adsnasa
94. M. A. Korolev, “Raspredelenie ratsionalnykh tochek na edinichnoi okruzhnosti (po sovmestnoi rabote s A. V. Ustinovym)”, Materialy IV Mezhdunarodnoi nauchnoi konferentsii "Aktualnye problemy prikladnoi matematiki (Kabardino-Balkarskaya respublika, pos.Terskol, 22–26 maya 2018 g.), IPMA KBNTs RAN, Nalchik, 2018, 130
95. M. A. Korolev, “Ob odnom raspredelenii, svyazannom s drobyami Fareya”, "Algebra, teoriya chisel i diskretnaya geometriya: sovremennye problemy i prilozheniya. Materialy XV Mezhdunarodnoi konferentsii, posvyaschennoi stoletiyu so dnya rozhdeniya professora Nikolaya Mikhailovicha Korobova (Tula, 28–31 maya 2018 g.), Seriya “Biblioteka Chebyshevskogo sbornika”, TPGU im. L.N. Tolstogo, Tula, 2018, 34-36
96. M. A. Korolev, “The estimate of weighted Kloosterman sums by additive shift”, Chebyshevskii Sb., 19:3 (2018), 183–201  mathnet  crossref  elib
97. I. D. Shkredov, “An application of the sum-product phenomenon to sets avoiding several linear equations”, Sb. Math., 209:4 (2018), 580–603  mathnet  crossref  crossref  mathscinet  adsnasa  isi (cited: 2)  elib  scopus (cited: 3)
98. I.D. Shkredov, “Differences of subgroups in subgroups”, Int. J. Number Theory, 14:4 (2018), 1111–1134 , arXiv: 1508.03814  mathnet  crossref  mathscinet  isi (cited: 1)  scopus (cited: 5)
99. Garmonicheskii analiz, teoriya priblizhenii i teoriya chisel, Sbornik statei. K 60-letiyu so dnya rozhdeniya akademika Sergeya Vladimirovicha Konyagina, Trudy MIAN, 303, ed. B. S. Kashin, Yu. V. Malykhin, V. Yu. Protasov, I. D. Shkredov, K. S. Ryutin, MAIK Nauka/Interperiodika, M., 2018 , 287 pp.  mathnet
100. Ilya D. Shkredov, Dmitrii Zhelezov, “On additive bases of sets with small product set”, Int. Math. Res. Not. IMRN, 2018:5 (2018), 1585–1599  mathnet  crossref  mathscinet  isi (cited: 5)  scopus (cited: 7)
101. I. D. Shkredov, I. E. Shparlinski, “Double character sums with intervals and arbitrary sets”, Proc. Steklov Inst. Math., 303 (2018), 239–258  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 2)  elib  scopus (cited: 2)
102. Misha Rudnev, Ilya D. Shkredov, “On the restriction problem for discrete paraboloid in lower dimension”, Adv. Math., 339 (2018), 657–671  mathnet  crossref  mathscinet  zmath  isi (cited: 8)  scopus (cited: 7)
103. Oliver Roche-Newton, Ilya D. Shkredov, Arne Winterhof, “Packing sets over finite abelian groups”, Integers, 18 (2018), A38 , 9 pp.  mathnet  mathscinet  zmath
104. B. S. Kashin, Yu. V. Malykhin, V. Yu. Protasov, K. S. Ryutin, I. D. Shkredov, “Sergei Vladimirovich Konyagin turns 60”, Proc. Steklov Inst. Math., 303 (2018), 1–9  mathnet  crossref  crossref  mathscinet  isi  elib  scopus
105. I. D. Shkredov, “On asymptotic formulae in some sum-product questions”, Trans. Moscow Math. Soc., 2018, 231–281  mathnet  crossref  mathscinet  zmath  elib  scopus (cited: 17)
106. Simon Macourt, Ilya D. Shkredov, Igor E. Shparlinski, “Multiplicative energy of shifted subgroups and bounds on exponential sums with trinomials in finite fields”, Can. J. Math., 70:6 (2018), 1319–1338  mathnet  crossref  mathscinet  zmath  isi (cited: 7)  scopus (cited: 9)
107. Olga Balkanova, Dmitry Frolenkov, “Non-vanishing of automorphic $L$-functions of prime power level”, Monatsh. Math., 185:1 (2018), 17–41 , arXiv: 1605.02434  mathnet  crossref  mathscinet  isi (cited: 2)  scopus (cited: 2)
108. Olga Balkanova, Dmitry Frolenkov, “The mean value of symmetric square $L$-functions”, Algebra Number Theory, 12:1 (2018), 35–59 , arXiv: 1610.06331  mathnet  crossref  mathscinet  isi (cited: 7)  scopus (cited: 9)
109. A. O. Radomskii, “On approximation characteristics of some classes of functions of small smoothness”, Siberian Math. J., 59:3 (2018), 486–493  mathnet  crossref  crossref  mathscinet  isi  elib  scopus
110. A. O. Radomskii, “Some properties of the space of quasi-continuous functions”, Russian Math. Surveys, 73:6 (2018), 1119–1121  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus (cited: 1)
111. M. R. Gabdullin, “Sets in $\mathbb{Z}_m$ whose difference sets avoid squares”, Sb. Math., 209:11 (2018), 1603–1610  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
112. M. R. Gabdullin, “Estimates for character sums in finite fields of order $p^2$ and $p^3$”, Proc. Steklov Inst. Math., 303 (2018), 36–49  mathnet  crossref  crossref  mathscinet  mathscinet  mathscinet  zmath  isi  elib  scopus

113. S. V. Konyagin, M. A. Korolev, “Irreducible solutions of an equation involving reciprocals”, Sb. Math., 208:12 (2017), 1818–1834  mathnet  crossref  crossref  mathscinet  adsnasa  isi (cited: 5)  elib  scopus (cited: 1)
114. Kevin Ford, Moubariz Z. Garaev, Sergei V. Konyagin, “On the smallest simultaneous power nonresidue modulo a prime”, Forum Math., 29:2 (2017), 347–355  mathnet  crossref  mathscinet  isi (cited: 1)  scopus (cited: 1)
115. Analiticheskaya teoriya chisel, Sbornik statei. K 80-letiyu so dnya rozhdeniya Anatoliya Alekseevicha Karatsuby, Trudy MIAN, 299, ed. M. A. Korolev, A. G. Sergeev, MAIK Nauka/Interperiodika, M., 2017 , 303 pp.  mathnet
116. M. A. Korolev, “On Anatolii Alekseevich Karatsuba's works written in the 1990s and 2000s”, Proc. Steklov Inst. Math., 299 (2017), 1–43  mathnet  crossref  crossref  mathscinet  isi  elib  elib  scopus
117. M. A. Korolev, “Generalized Kloosterman sum with primes”, Proc. Steklov Inst. Math., 296 (2017), 154–171  mathnet  crossref  crossref  mathscinet  isi (cited: 6)  elib  scopus (cited: 6)  scopus (cited: 6)
118. K. Gong, C. Jia, M.A. Korolev, “Shifted character sums with multiplicative coefficients, II”, J. Number Theory, 178 (2017), 31–39 , arXiv: 1611.06577v1  mathnet  crossref  mathscinet  isi (cited: 1)  elib  scopus (cited: 2)
119. M. A. Korolev, “On a Diophantine inequality with reciprocals”, Proc. Steklov Inst. Math., 299 (2017), 132–142  mathnet  crossref  crossref  mathscinet  isi (cited: 5)  elib  elib  scopus (cited: 2)
120. M. A. Korolev, “On the estimates of Kloosterman sums”, Vilnius Conference in Combinatoris and Number Theory, Program and Abstract book (Vilnius, Lithuania, July 16 - July 22, 2017), Vilnius University, 2017, p. 14. http://mjcnt.phystech.edu/conference/vilnius/Vilnius2017.pdf
121. M. A. Korolëv, “Obratnye vychety v posledovatelnosti Pyatetskogo-Shapiro”, Konferentsiya po teorii chisel i prilozheniyam v chest 80-letiya A.A.Karatsuby, Sbornik annotatsii (Moskva, 22 - 27 maya 2017 g.), eds. M. A. Korolëv, OOO “Poligraff”, 2017, s. 34. http://www.mathnet.ru/ConfLogos/936/abstracts.pdf

122. M. A. Korolev, “On Rieman–Siegel formula for the derivatives of Hardy's function”, St. Petersburg Math. J., 29:4 (2018), 581–601  mathnet  crossref  mathscinet  mathscinet  isi (cited: 1)  elib  scopus (cited: 1)

123. I. V. Vyugin, E. V. Solodkova, I. D. Shkredov, “On the Additive Energy of the Heilbronn Subgroup”, Math. Notes, 101:1 (2017), 58–70  mathnet  crossref  crossref  mathscinet  isi (cited: 1)  elib  scopus (cited: 1)
124. Orit E. Raz, Micha Sharir, Ilya D. Shkredov, “On the number of unit-area triangles spanned by convex grids in the plane”, Comput. Geom., 62:1 (2017), 25–33  mathnet  crossref  mathscinet  isi (cited: 1)  elib  scopus (cited: 3)
125. A. S. Volostnov, I. D. Shkredov, “Sums of Multiplicative Characters with Additive Convolutions”, Proc. Steklov Inst. Math., 296 (2017), 256–269  mathnet  crossref  crossref  mathscinet  isi (cited: 7)  elib  scopus (cited: 8)  scopus (cited: 8)
126. I. D. Shkredov, “Some remarks on sets with small quotient set”, Sb. Math., 208:12 (2017), 1854–1868  mathnet  crossref  crossref  mathscinet  adsnasa  isi (cited: 6)  elib  scopus (cited: 7)
127. I. D. Shkredov, “Some Remarks on the Balog–Wooley Decomposition Theorem and Quantities $D^{+}$, $D^\times$”, Proc. Steklov Inst. Math., 298, suppl. 1 (2017), 74–90  mathnet  crossref  crossref  mathscinet  mathscinet  isi (cited: 3)  elib  scopus (cited: 5)
128. Esen Aksoy Yazici, Brendan Murphy, Misha Rudnev, Ilya Shkredov, “Growth estimates in positive characteristic via collisions”, Int. Math. Res. Not. IMRN, 2017:23 (2017), 7148 , 7189 pp., arXiv: 1512.06613  mathnet  crossref  mathscinet  isi (cited: 23)  scopus (cited: 21)
129. Ilya D. Shkredov, Igor E. Shparlinski, “On some multiple character sums”, Mathematika, 53:2 (2017), 553–560  mathnet  crossref  mathscinet  isi (cited: 3)  scopus (cited: 3)
130. B. Murphy, O. Roche-Newton, I. D. Shkredov, “Variations on the sum-product problem II”, SIAM J. Discrete Math., 31:3 (2017), 1878–1894 , arXiv: 1703.09549  mathnet  crossref  mathscinet  isi (cited: 6)  elib  scopus (cited: 12)
131. I. S. Rezvyakova, “Additive Problem with the Coefficients of Hecke $L$-Functions”, Proc. Steklov Inst. Math., 296 (2017), 234–242  mathnet  crossref  crossref  mathscinet  isi (cited: 1)  elib  scopus  scopus
132. Olga Balkanova, Dmitry Frolenkov, “New error term for the fourth moment of automorphic $L$-functions”, J. Number Theory, 173 (2017), 293–303  mathnet  crossref  mathscinet  zmath  isi (cited: 2)  scopus (cited: 2)
133. V. A. Bykovskii, D. A. Frolenkov, “Asymptotic formulae for the second moments of $L$-series of holomorphic cusp forms on the critical line”, Izv. Math., 81:2 (2017), 239–268  mathnet  crossref  crossref  mathscinet  adsnasa  isi (cited: 4)  elib  elib  scopus (cited: 2)
134. Olga G. Balkanova, Dmitry A. Frolenkov, “On the binary additive divisor problem”, Proc. Steklov Inst. Math., 299 (2017), 44–49  mathnet  crossref  crossref  mathscinet  mathscinet  mathscinet  isi (cited: 1)  elib  scopus (cited: 1)
135. V. A. Bykovskii, D. A. Frolenkov, “The average length of finite continued fractions with fixed denominator”, Sb. Math., 208:5 (2017), 644–683  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib  scopus
136. Olga Balkanova, Dmitry Frolenkov, “The first moment of cusp form $L$-functions in weight aspect on average”, Acta Arith., 181:3 (2017), 197–208 , arXiv: 1703.00742  mathnet  crossref  mathscinet  isi (cited: 2)  scopus (cited: 2)
137. A. O. Radomskii, “On a Sidon-type Inequality for Discrete Orthonormal Systems”, Math. Notes, 101:4 (2017), 693–698  mathnet  crossref  crossref  mathscinet  isi (cited: 3)  elib  scopus (cited: 1)

138. A. O. Radomskii, “On the Sidon inequality for trigonometric polynomials”, St. Petersburg Math. J., 29:4 (2018), 643–656  mathnet  crossref  mathscinet  isi (cited: 3)  elib  scopus (cited: 2)

139. Sergei V. Konyagin, Florian Luca, Bernard Mans, Luke Mathieson, Min Sha, Igor E. Shparlinski, “Functional graphs of polynomials over finite fields”, J. Comb. Theory, Ser. B, 116 (2016), 87–122 , arXiv: 1307.2718  mathnet  crossref  mathscinet  zmath  isi (cited: 11)  elib  scopus (cited: 12)
140. Kevin Ford, Ben Green, Sergei Konyagin, Terence Tao, “Large gaps between consecutive prime numbers”, Ann. of Math. (2), 183:3 (2016), 935–974 , arXiv: 1408.4505  mathnet  crossref  mathscinet  zmath  isi (cited: 14)  elib  scopus (cited: 17)
141. S. V. Konyagin, A. A. Kuleshov, “On some properties of finite sums of ridge functions defined on convex subsets of $\mathbb R^n$”, Proc. Steklov Inst. Math., 293 (2016), 186–193  mathnet  crossref  crossref  mathscinet  isi (cited: 8)  elib  elib  scopus (cited: 3)
142. S. V. Konyagin, M. A. Korolev, “On a symmetric diophantine equation with reciprocals”, Proc. Steklov Inst. Math., 294 (2016), 67–77  mathnet  crossref  crossref  mathscinet  isi (cited: 7)  elib  elib  scopus (cited: 4)
143. S. V. Konyagin, I. D. Shkredov, “New results on sums and products in $\mathbb R$”, Proc. Steklov Inst. Math., 294 (2016), 78–88 , arXiv: 1602.03473  mathnet  crossref  crossref  mathscinet  isi (cited: 26)  elib  elib  scopus (cited: 25)

144. A. A. Karatsuba, “Cosmology and zeta”, Proc. Steklov Inst. Math., 296, suppl. 2 (2017), 11–17  mathnet  crossref  crossref  isi (cited: 1)  elib  elib  scopus
145. A. A. Karatsuba, “On zeros of certain Dirichlet series”, Proc. Steklov Inst. Math., 296, suppl. 2 (2017), 6–10  mathnet  crossref  crossref  isi (cited: 1)  elib  elib  scopus
146. A. A. Karatsuba, “On local representation of zero by a form”, Proc. Steklov Inst. Math., 296, suppl. 2 (2017), 1–5  mathnet  crossref  crossref  isi (cited: 1)  elib  scopus

147. M. A. Korolev, “On non-linear Kloosterman sum”, Chebyshevskii Sb., 17:1 (2016), 140–147  mathnet  mathscinet  mathscinet  elib
148. M. A. Korolev, “Karatsuba's method for estimating Kloosterman sums”, Sb. Math., 207:8 (2016), 1142–1158  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 10)  elib  elib  scopus (cited: 2)
149. M. A. Korolev, On Kloosterman sums with multiplicative coefficients, 2016 , 13 pp., arXiv: 1610.09171
150. M. A. Korolev, “Short Kloosterman Sums to Powerful Modulus”, Doklady Mathematics, 94:2 (2016), 561–562  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 5)  elib  elib  scopus (cited: 3)
151. M. A. Korolev, “Gram's Law in the Theory of Riemann Zeta-Function. Part 2”, Proc. Steklov Inst. Math., 294, suppl. 1 (2016), 1–78  mathnet  crossref  crossref  mathscinet  isi (cited: 2)  elib  elib  scopus (cited: 2)
152. M. A. Korolev, “On Short Kloosterman Sums Modulo a Prime”, Math. Notes, 100:6 (2016), 820–827  mathnet  crossref  crossref  mathscinet  isi (cited: 8)  elib  elib  scopus (cited: 8)
153. M. A. Korolev, “Methods of estimating of incomplete Kloosterman sums”, Chebyshevskii Sb., 17:4 (2016), 79–109  mathnet  crossref  mathscinet  elib
154. Maxim Aleksandrovich Korolev, “An extreme values of the function S(T) in short intervals”, Indian J. Pure Appl. Math., 47:4 (2016), 603–615 , arXiv: 1302.0352  mathnet  crossref  mathscinet  zmath  isi  scopus
155. Tomasz Schoen, Ilya D. Shkredov, “Additive dimension and a theorem of sanders”, J. Aust. Math. Soc., 100:1 (2016), 124–144  mathnet  crossref  mathscinet  isi (cited: 4)  elib  scopus (cited: 3)
156. S. V. Konyagin, I. D. Shkredov, New results on sum–products in $\mathbb R$, 2016 , 18 pp., arXiv: 1602.03473  mathscinet
157. Ilya D. Shkredov, “On a question of A. Balog”, Pacific J. Math., 280:1 (2016), 227–240  mathnet  crossref  mathscinet  zmath  isi (cited: 6)  elib  scopus (cited: 7)
158. Oliver Roche-Newton, Misha Rudnev, Ilya D. Shkredov, “New sum-product type estimates over finite fields”, Adv. Math., 293 (2016), 589–605  mathnet (cited: 4)  crossref  mathscinet  zmath  isi (cited: 35)  elib  scopus (cited: 43)
159. Alex Samorodnitsky, Ilya Shkredov, Sergey Yekhanin, “Kolmogorov width of discrete linear spaces: An approach to matrix rigidity”, Comput. Complexity, 25:2 (2016), 309–348  mathnet  crossref  mathscinet  zmath  isi  elib  scopus (cited: 1)
160. I. V. Vyugin, E. V. Solodkova, I. D. Shkredov, “Intersections of Shifts of Multiplicative Subgroups”, Math. Notes, 100:2 (2016), 189–198  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 4)  elib  elib  scopus (cited: 4)
161. I. D. Shkredov, “Erratum to: On some problems of Euclidean Ramsey theory”, Anal. Math., 42:3 (2016), 295  mathnet  crossref  mathscinet  isi  scopus
162. I. D. Shkredov, Some remarks on sets with small quotient set, 2016 , 14 pp., arXiv: 1603.04948v2
163. Shkredov, I. D., “Difference sets are not multiplicatively closed”, Discrete Anal., 2016, 17 , 21 pp.  mathnet  crossref  mathscinet  scopus (cited: 12)
164. I.D. Shkredov, “On tripling constant of multiplicative subgroups”, Integers, 16 (2016), 75 , 9 pp.  mathnet  mathscinet
165. Tomasz Schoen, Ilya D. Shkredov, “A remark on $A+B$ and $A-A$ for compact sets in $\mathbb R^n$”, Integers, 16 (2016), 60 , 4 pp.  mathnet  mathscinet
166. I. S. Rezvyakova, “On the zeros of linear combinations of L-functions of degree two on the critical line. Selberg's approach”, Izv. Math., 80:3 (2016), 602–622  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 4)  elib  elib  scopus (cited: 1)
167. Olga G. Balkanova, Dmitry A. Frolenkov, “A uniform asymptotic formula for the second moment of primitive $L$-functions on the critical line”, Proc. Steklov Inst. Math., 294 (2016), 13–46  mathnet  crossref  crossref  mathscinet  isi (cited: 5)  elib  elib  scopus (cited: 4)
168. A. O. Radomskii, “On nonequivalence of the $\mathrm{C}$- and $\mathrm{QC}$-norms in the space of trigonometric polynomials”, Sb. Math., 207:12 (2016), 1729–1742  mathnet  crossref  crossref  mathscinet  adsnasa  isi (cited: 3)  elib  elib  scopus (cited: 3)
169. M. R. Gabdullin, “On squares in special sets of finite fields”, Chebyshevskii Sb., 17:2 (2016), 56–63  mathnet  crossref  mathscinet  zmath  elib

170. M. R. Gabdullin, “On the Squares in the Set of Elements of a Finite Field with Constraints on the Coefficients of Its Basis Expansion”, Math. Notes, 101:2 (2017), 234–249  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 4)  elib  elib  scopus

171. M. R. Gabdullin, “On the Divergence of Fourier Series in the Spaces $\varphi(L)$ Containing $L$”, Math. Notes, 99:6 (2016), 861–869  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus
172. Olga Balkanova, “The shifted fourth moment of automorphic L-functions of prime power level”, Acta Arith., 174 (2016), 121–174  crossref  mathscinet  zmath  isi (cited: 1)  scopus (cited: 1)

173. S. R. Blackburn, S. V. Konyagin, I. E. Shparlinski, “Counting additive decompositions of quadratic residues in finite fields”, Funct. Approx. Comment. Math., 52:2 (2015), 223–227  mathnet  crossref  mathscinet  zmath  elib  scopus (cited: 1)
174. S. V. Konyagin, I. D. Shkredov, “A quantitative version of the Beurling-Helson theorem”, Funct. Anal. Appl., 49:2 (2015), 110–121 , arXiv: 1401.4429  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 4)  elib  elib  scopus (cited: 5)
175. S. V. Konyagin, A. A. Kuleshov, “On the Continuity of Finite Sums of Ridge Functions”, Math. Notes, 98:2 (2015), 336–338  mathnet  crossref  crossref  mathscinet  isi (cited: 10)  elib  elib  scopus (cited: 3)
176. S. V. Konyagin, I. E. Shparlinski, “Quadratic non-residues in short intervals”, Proc. Amer. Math. Soc., 143:10 (2015), 4261–4269  mathnet  crossref  mathscinet  zmath  isi (cited: 2)  elib  scopus (cited: 2)
177. S. V. Konyagin, I. D. Shkredov, “On Sum Sets of Sets Having Small Product Set”, Proc. Steklov Inst. Math., 290 (2015), 288–299  mathnet  crossref  crossref  isi (cited: 37)  elib  elib  scopus (cited: 31)
178. J. Bourgain, S. V. Konyagin, I. E. Shparlinski, “Character sums and deterministic polynomial root finding in finite fields”, Math. Comp., 84:296 (2015), 2969–2977 , arXiv: 1308.4803  mathnet  crossref  mathscinet  zmath  isi (cited: 6)  elib  scopus (cited: 7)
179. K. Ford, D. R. Heath-Brown, S. V. Konyagin, “Large gaps between consecutive prime numbers containing perfect powers”, Analytic Number Theory, In Honor of Helmut Maier's 60th Birthday, eds. C. Pomerance, M. Th. Rassias, Springer, New York, 2015, 83–92 , arXiv: 1411.6543  mathnet  crossref  mathscinet  zmath  scopus (cited: 5)
180. A. A. Karatsuba, “Vienna talk: on the number of zeros of the Riemann zeta function in short intervals of the critical line”, Chebyshevskii Sb., 16:1 (2015), 19–31  mathnet  elib
181. A. A. Karatsuba, “Moscow talk: the theorem on approximation of trigonometric sum by a short one (ATS)”, Chebyshevskii Sb., 16:1 (2015), 6–18  mathnet  elib
182. M. A. Korolev, “Large values of the Riemann zeta-function on short intervals of the critical line”, Dokl. Math., 91:1 (2015), 102–104  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 1)  elib  elib  scopus (cited: 1)
183. E. A. Karatsuba, M. A. Korolev, I. S. Rezvyakova, V. N. Chubarikov, “On the conference to the memory of Anatoly Alexeevitch Karatsuba on number theory and applications”, Chebyshevskii Sb., 16:1 (2015), 89–152  mathnet  mathscinet  elib
184. M. A. Korolev, “On Incomplete Gaussian Sums”, Proc. Steklov Inst. Math., 290 (2015), 52–62  mathnet  crossref  crossref  isi (cited: 5)  elib  elib  scopus (cited: 2)
185. M. A. Korolev, “On the Horizontal Distribution of Zeros of the Functions $\operatorname{Re} \zeta(s)$ and $\operatorname{Im}\zeta(s)$”, Math. Notes, 98:6 (2015), 986–989  mathnet  crossref  crossref  mathscinet  isi  elib  elib  scopus

186. M. A. Korolev, “Gram's Law in the Theory of Riemann Zeta-Function. Part 1”, Proc. Steklov Inst. Math., 292, suppl. 2 (2016), S1–S146  mathnet  mathnet  crossref  crossref  crossref  mathscinet  isi (cited: 5)  elib  elib  scopus (cited: 5)

187. M. A. Korolev, “On the primitive of Hardy's function”, The 29th Journees Arithmetiques. Conference handbook (University of Debrecen, Hungary, July 6–10, 2015), University of Debrecen, 2015, 57–58 http://www.ja2015.math.unideb.hu/sites/default/files/Abstracts.pdf
188. M. A. Korolev, “On the large values of the Riemann zeta-function on the critical line II”, Moscow J. Combin. Number Theory, 5:3 (2015), 60–86 , arXiv: 1412.6340  mathnet  mathscinet  zmath  adsnasa
189. I. D. Shkredov, “Structure theorems in additive combinatorics”, Russian Math. Surveys, 70:1 (2015), 113–163  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib  scopus
190. Brendan Murphy, Oliver Roche-Newton, Ilya Shkredov, “Variations on the sum-product problem”, SIAM J. Discrete Math., 29:1 (2015), 514–540  mathnet (cited: 1)  crossref  mathscinet  zmath  isi (cited: 17)  elib (cited: 1)  scopus (cited: 19)
191. I. D. Shkredov, “On Sums of Szemerédi–Trotter Sets”, Proc. Steklov Inst. Math., 289 (2015), 300–309  mathnet  crossref  crossref  isi (cited: 14)  elib  elib  scopus (cited: 14)
192. I. D. Shkredov, “On some problems of Euclidean Ramsey theory”, Anal. Math., 41:4 (2015), 299–310  mathnet  crossref  mathscinet  zmath  isi (cited: 1)  elib  scopus
193. G. I. Arkhipov, V. N. Chubarikov, “Anatoly Alekseevich Karatsuba”, Chebyshevskii Sb., 16:1 (2015), 32–51  mathnet  mathscinet  elib
194. I. S. Rezvyakova, “Selbergs method in the problem about the zeros of linear combinations of $L$-functions on the critical line”, Dokl. Math., 92:1 (2015), 448–451  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 1)  elib  elib  scopus
195. I. S. Rezvyakova, “On the zeros of the Epstein zeta-function on the critical line”, Russian Math. Surveys, 70:4 (2015), 785–787  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 4)  elib  elib  scopus (cited: 2)
196. V. A. Bykovskii, D. A. Frolenkov, “Some integral representations of hypergeometric function”, FEMJ, 15:1 (2015), 38–40  mathnet  elib
197. D. A. Frolenkov, “On the uniform bounds on hypergeometric function”, Dal'nevost. Mat. Zh., 15:2 (2015), 289–298  mathnet  elib
198. V. A. Bykovskii, D. A. Frolenkov, “On the second moment of L-series of holomorphic cusp forms on the critical line”, Dokl. Math., 92:1 (2015), 417–420  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 2)  elib  elib  scopus (cited: 1)
199. V. A. Bykovskii, D. A. Frolenkov, “Asymptotic formula for the convolution of a generalized divisor function”, Dokl. Math., 92:3 (2015), 670–673  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 1)  elib  elib  scopus (cited: 1)
200. A. O. Radomskii, “QC-norm of trigonometric polynomials of special form”, Moscow University Math. Bull., 70:2 (2015), 84–87  mathnet  crossref  mathscinet  zmath  isi  elib  elib  scopus (cited: 1)
201. P. G. Grigor'ev, A. O. Radomskii, “Some Trigonometric Polynomials with Extremally Small Uniform Norm”, Math. Notes, 98:2 (2015), 230–236  mathnet  crossref  crossref  mathscinet  isi (cited: 2)  elib  scopus (cited: 2)

202. M. R. Gabdullin, “On the divergence of trigonometric Fourier series in classes $\varphi(L)$ contained in $L$”, Proc. Steklov Inst. Math. (Suppl.), 297, suppl. 1 (2017), 81–87  mathnet  crossref  mathscinet  isi  elib  scopus
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