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



   2019
1. Ilya D. Shkredov, “Some remarks on the asymmetric sum–product phenomenon”, Moscow J. Combin. Number Theory, 8:1 (2019), 15–41  mathnet  crossref  mathscinet
2. I. D. Shkredov, “A short note on the multiplicative energy of the spectrum of a set”, Mat. Zametki  mathnet  crossref  elib

   2019
3. Oliver Roche-Newton, Ilya D. Shkredov, “If $A+A$ is small then $AAA$ is superquadratic”, J. Number Theory, 201 (2019), 124–134  mathnet  crossref  isi  scopus

   2018
4. 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: 1)  elib  scopus (cited: 1)
5. 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  scopus (cited: 1)
6. I.D. Shkredov, “Differences of subgroups in subgroups”, Int. J. Number Theory, 14:4 (2018), 1111–1134 , arXiv: 1508.03814  mathnet  crossref  mathscinet  isi  scopus (cited: 4)
7. Garmonicheskii analiz, teoriya priblizhenii i teoriya chisel, Sbornik statei. K 60-letiyu so dnya rozhdeniya akademika Sergeya Vladimirovicha Konyagina, Tr. 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
8. 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: 3)  scopus (cited: 5)
9. 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  isi  elib  scopus
10. Misha Rudnev, Ilya D. Shkredov, “On the restriction problem for discrete paraboloid in lower dimension”, Adv. Math., 339 (2018), 657–671  mathnet  crossref  mathscinet  isi  scopus
11. Oliver Roche-Newton, Ilya D. Shkredov, Arne Winterhof, “Packing sets over finite abelian groups”, Integers, 18 (2018), A38 , 9 pp.  mathnet  mathscinet
12. 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  isi  elib  scopus
13. I. D. Shkredov, “On asymptotic formulae in some sum-product questions”, Trans. Moscow Math. Soc., 2018, 231–281  mathnet  crossref  elib  scopus (cited: 2)
14. 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  isi (cited: 2)  scopus (cited: 3)

   2017
15. 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  elib  scopus
16. 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: 2)
17. 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: 3)  elib  scopus (cited: 4)  scopus (cited: 4)
18. 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: 3)  elib  scopus (cited: 3)
19. 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  isi  elib  scopus (cited: 1)
20. 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: 17)  scopus (cited: 14)
21. Ilya D. Shkredov, Igor E. Shparlinski, “On some multiple character sums”, Mathematika, 53:2 (2017), 553–560  mathnet  crossref  mathscinet  isi (cited: 2)  scopus (cited: 2)
22. 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: 4)  scopus (cited: 7)

   2016
23. 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: 3)  elib  scopus (cited: 2)
24. S. V. Konyagin, I. D. Shkredov, New results on sum–products in $\mathbb R$, 2016 , 18 pp., arXiv: 1602.03473
25. 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)
26. Oliver Roche-Newton, Misha Rudnev, Ilya D. Shkredov, “New sum-product type estimates over finite fields”, Adv. Math., 293 (2016), 589–605  mathnet (cited: 3)  crossref  mathscinet  zmath  isi (cited: 24)  elib  scopus (cited: 31)
27. 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
28. 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: 2)  elib  elib  scopus (cited: 2)
29. 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: 17)  elib  elib  scopus (cited: 19)
30. I. D. Shkredov, “Erratum to: On some problems of Euclidean Ramsey theory”, Anal. Math., 42:3 (2016), 295  mathnet  crossref  isi  scopus
31. I. D. Shkredov, Some remarks on sets with small quotient set, 2016 , 14 pp., arXiv: 1603.04948v2
32. Shkredov, I. D., “Difference sets are not multiplicatively closed”, Discrete Anal., 2016, 17 , 21 pp.  mathnet  crossref  scopus (cited: 10)
33. I.D. Shkredov, “On tripling constant of multiplicative subgroups”, Integers, 16 (2016), 75 , 9 pp.  mathnet
34. 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

   2015
35. 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
36. 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: 11)  elib (cited: 1)  scopus (cited: 11)
37. I. D. Shkredov, “On Sums of Szemerédi–Trotter Sets”, Proc. Steklov Inst. Math., 289 (2015), 300–309  mathnet  crossref  crossref  isi (cited: 7)  elib  elib  scopus (cited: 8)
38. 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: 1)  elib  elib  scopus (cited: 1)
39. 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: 29)  elib  elib  scopus (cited: 25)
40. I. D. Shkredov, “On some problems of Euclidean Ramsey theory”, Anal. Math., 41:4 (2015), 299–310  mathnet  crossref  mathscinet  zmath  isi (cited: 1)  scopus

   2014
41. 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: 7)  scopus (cited: 7)
42. I. D. Shkredov, “Sumsets in quadratic residues”, Acta Arith., 164:3 (2014), 221–243 , arXiv: 1305.4093v1  mathnet  crossref  mathscinet  zmath  isi (cited: 12)  elib (cited: 3)  scopus (cited: 12)
43. 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: 16)  elib (cited: 8)  scopus (cited: 15)
44. I. Shkredov, “Energies and structure of additive sets”, Electron. J. Combin., 21:3 (2014), P3.44 , 53 pp.  mathnet  mathscinet  zmath  isi  scopus (cited: 9)

   2016
45. 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  scopus

   2013
46. T. Schoen, I. D. Shkredov, “Higher moments of convolutions”, J. Number Theory, 133 (2013), 1693–1737  mathnet  crossref  mathscinet  zmath  isi (cited: 20)  elib (cited: 15)  scopus (cited: 25)
47. I. D. Shkredov, On exponential sums over multiplicative subgroups of medium size, 2013 , 14 pp., arXiv: 1311.5726
48. I. D. Shkredov, New bounds for Heilbronn's exponential sum, 2013 , 14 pp., arXiv: 1302.3839
49. I. D. Shkredov, “Some new results on higher energies”, Trans. Moscow Math. Soc., 2013 (2013), 31–63  mathnet  crossref  mathscinet  zmath  elib  scopus (cited: 11)
50. 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: 11)
51. 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
52. 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: 14)  elib (cited: 11)  scopus (cited: 16)
53. 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: 20)  elib (cited: 6)  elib (cited: 6)  scopus (cited: 7)
54. 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
55. 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: 6)  elib (cited: 3)  scopus (cited: 5)
56. I. D. Shkredov, T. Schoen, “On sumsets of convex sets”, Comb. Probab. Comput., 20 (2011), 793–798  crossref  mathscinet  zmath  isi (cited: 16)  elib (cited: 16)  scopus (cited: 22)
57. 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

   2010
58. 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: 7)  elib (cited: 6)  elib (cited: 6)  scopus (cited: 8)
59. 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: 1)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 1)

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

   2010
61. 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


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