Home page
Home page
Home page
Russian page
English page
Math-Net.Ru | MMS | Web of Science | Scopus | MathSciNet | zbMATH | Web-mail 

   
 About the Institute
 Staff publications
 Administration
 Academic Council
 Dissertation Councils
 Departments
Staff 
 Chair at MIPT
 Seminars
 Conferences
 Events
 Journals and Books
 In memoriam
 Photogallery
 Charter


    Address
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

View Map
Directions

   
Shkredov Ilya Dmitrievich
(recent publications)
| by years | scientific publications | by types |


1. I. D. Shkredov, Uspekhi Mat. Nauk (to appear)  mathnet

   2021
2. I. D. Shkredov, “Modular hyperbolas and bilinear forms of Kloosterman sums”, J. Number Theory, 220 (2021), 182–211  mathnet  crossref  isi  scopus;
3. 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

   2020
4. 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
5. 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);
6. 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);
7. 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);
8. T. Schoen, I. D. Shkredov, “$L$-functions and sum-free sets”, Acta Math. Hung., 161 (2020), 427–442  mathnet  crossref  mathscinet  isi  scopus;
9. 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
10. 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);
11. 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);
12. 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);
13. 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)

   2019
14. 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)
15. 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
16. 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)
17. 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)
18. 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)
19. 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)
20. 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);
21. 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);
22. 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);

   2018
23. 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)
24. 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)
25. 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)
26. 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
27. 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)
28. 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)
29. 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)
30. Oliver Roche-Newton, Ilya D. Shkredov, Arne Winterhof, “Packing sets over finite abelian groups”, Integers, 18 (2018), A38 , 9 pp.  mathnet  mathscinet  zmath
31. 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
32. 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)
33. 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)

   2017
34. 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)
35. 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)
36. 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)
37. 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)
38. 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)
39. 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)
40. 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)
41. 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)

   2016
42. 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)
43. S. V. Konyagin, I. D. Shkredov, New results on sum–products in $\mathbb R$, 2016 , 18 pp., arXiv: 1602.03473  mathscinet
44. 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)
45. 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)
46. 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)
47. 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)
48. S. V. Konyagin, I. D. Shkredov, “New results on sums and products in $\mathbb R$”, Proc. Steklov Inst. Math., 294 (2016), 78–88  mathnet  crossref  crossref  mathscinet  isi (cited: 26)  elib  elib  scopus (cited: 25)
49. I. D. Shkredov, “Erratum to: On some problems of Euclidean Ramsey theory”, Anal. Math., 42:3 (2016), 295  mathnet  crossref  mathscinet  isi  scopus
50. I. D. Shkredov, Some remarks on sets with small quotient set, 2016 , 14 pp., arXiv: 1603.04948v2
51. Shkredov, I. D., “Difference sets are not multiplicatively closed”, Discrete Anal., 2016, 17 , 21 pp.  mathnet  crossref  mathscinet  scopus (cited: 12)
52. I.D. Shkredov, “On tripling constant of multiplicative subgroups”, Integers, 16 (2016), 75 , 9 pp.  mathnet  mathscinet
53. 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

   2015
54. 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
55. 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)
56. 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)
57. S. V. Konyagin, I. D. Shkredov, “A quantitative version of the Beurling-Helson theorem”, Funct. Anal. Appl., 49:2 (2015), 110–121  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 4)  elib  elib  scopus (cited: 5)
58. 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)
59. 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

   2014
60. T. Schoen, I. D. Shkredov, “Roth's theorem in many variables”, Israel J. Math., 199:1 (2014), 287–308 , arXiv: 1106.1601v1  mathnet  crossref  mathscinet  zmath  isi (cited: 8)  elib  scopus (cited: 9)
61. I. D. Shkredov, “Sumsets in quadratic residues”, Acta Arith., 164:3 (2014), 221–243 , arXiv: 1305.4093v1  mathnet  crossref  mathscinet  zmath  isi (cited: 16)  elib (cited: 3)  scopus (cited: 17)
62. I. D. Shkredov, “On exponential sums over multiplicative subgroups of medium size”, Finite Fields Appl., 30 (2014), 72–87  mathnet  crossref  mathscinet  zmath  isi (cited: 17)  elib (cited: 8)  scopus (cited: 18)
63. I. Shkredov, “Energies and structure of additive sets”, Electron. J. Combin., 21:3 (2014), P3.44 , 53 pp.  mathnet  mathscinet  zmath  isi  scopus (cited: 14)

   2016
64. S. V. Konyagin, I. D. Shkredov, “On the Wiener norm of subsets of $\mathbb Z_p$ of medium size”, J. Math. Sci., 218:5 (2016), 599–608  mathnet  crossref  mathscinet  zmath  elib  elib  scopus (cited: 3)  scopus (cited: 3)

   2013
65. T. Schoen, I. D. Shkredov, “Higher moments of convolutions”, J. Number Theory, 133 (2013), 1693–1737  mathnet  crossref  mathscinet  zmath  isi (cited: 30)  elib (cited: 15)  scopus (cited: 34)
66. I. D. Shkredov, On exponential sums over multiplicative subgroups of medium size, 2013 , 14 pp., arXiv: 1311.5726
67. I. D. Shkredov, New bounds for Heilbronn's exponential sum, 2013 , 14 pp., arXiv: 1302.3839
68. I. D. Shkredov, “Some new results on higher energies”, Trans. Moscow Math. Soc., 2013 (2013), 31–63  mathnet  crossref  mathscinet  zmath  elib  scopus (cited: 23)
69. I. D. Shkredov, “On Heilbronn's exponential sum”, Q. J. Math., 64:4 (2013), 1221–1230  mathnet  crossref  mathscinet  zmath  isi (cited: 10)  elib (cited: 7)  scopus (cited: 12)
70. I. D. Shkredov, “Some new inequalities in additive combinatorics”, Moscow J. Combin. Number Theory, 3:3 (2013), 189–239 , arXiv: 1208.2344v3  mathnet  elib

   2012
71. I. D. Shkredov, T. Schoen, “Additive properties of multiplicative subgroups of $F_p$”, Quart. J. Math., 63:3 (2012), 713–722  mathnet  crossref  mathscinet  zmath  isi (cited: 16)  elib (cited: 11)  scopus (cited: 18)
72. I. V. Vyugin, I. D. Shkredov, “On additive shifts of multiplicative subgroups”, Sb. Math., 203:6 (2012), 844–863  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 21)  elib (cited: 6)  elib (cited: 6)  scopus (cited: 8)
73. I. D. Shkredov, “On the Gowers Norms of Certain Functions”, Math. Notes, 92:4 (2012), 554–569  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus

   2011
74. I. D. Shkredov, S. Yekhanin, “Sets with large additive energy and symmetric sets”, J. Combin. Theory Ser. A, 118:3 (2011), 1086–1093  crossref  mathscinet  zmath  isi (cited: 7)  elib (cited: 3)  scopus (cited: 6)
75. I. D. Shkredov, T. Schoen, “On sumsets of convex sets”, Comb. Probab. Comput., 20 (2011), 793–798  crossref  mathscinet  zmath  isi (cited: 24)  elib (cited: 16)  scopus (cited: 33)
76. I. D. Shkredov, “Some applications of W. Rudins inequality to problems of combinatorial Number theory”, Uniform Distribution Theory, 6:2 (2011), 95–116 http://www.boku.ac.at/math/udt/vol06/no2/08Shkredov11-2.pdf  mathscinet  zmath

   2010
77. I. D. Shkredov, “On Monochromatic Solutions of Some Nonlinear Equations in $\mathbb Z/p\mathbb Z$”, Math. Notes, 88:4 (2010), 603–611  mathnet  crossref  crossref  mathscinet  isi (cited: 8)  elib (cited: 6)  elib (cited: 6)  scopus (cited: 16)
78. I. D. Shkredov, “Fourier analysis in combinatorial number theory”, Russian Math. Surveys, 65:3 (2010), 513–567  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 3)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 3)

   2012
79. I. D. Shkredov, “On the Pyatetskii-Shapiro normality criterion for continued fractions”, J. Math. Sci., 182:4 (2012), 567–575  mathnet  crossref  mathscinet  zmath  elib  elib  scopus (cited: 2)

   2010
80. S. V. Konyagin, I. D. Shkredov, “On one result of J. Bourgain”, Ukr. Math. J., 62:3 (2010), 380–419  crossref  mathscinet  zmath  isi  elib  scopus


Full list of publications
Home page

© Steklov Mathematical Institute of RAS, 2004–2021