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Shkredov Ilya Dmitrievich
(full list of publications)
| by years | scientific publications | by types |



   2018
1. I. D. Shkredov, “Prilozheniya teorii summ proizvedenii k mnozhestvam, izbegayuschim neskolko lineinykh uravnenii”, Matem. sb., 209 (2018) (to appear)  mathnet [I. D. Shkredov, “An application of the sum-product phenomenon to sets having no solutions to several linear equations”, Mat. Sb. (to appear)]

   2017
2. 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
3. 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  elib  scopus
4. 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  elib  scopus
5. I. D. Shkredov, “Neskolko zamechanii o mnozhestvakh s malym chastnym”, Matem. sb., 208:12 (2017), 144–158  mathnet  crossref [I. D. Shkredov, “Some remarks on sets with small quotient set”, Mat. Sb.]
6. 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  isi  elib

   2016
7. Tomasz Schoen, Ilya D. Shkredov, “Additive dimension and a theorem of sanders”, J. Aust. Math. Soc., 100:1 (2016), 124–144  mathnet  crossref  mathscinet (cited: 1)  isi (cited: 1)  elib  scopus
8. S. V. Konyagin, I. D. Shkredov, New results on sum–products in $\mathbb R$, 2016 , 18 pp., arXiv: 1602.03473
9. Ilya D. Shkredov, “On a question of A. Balog”, Pacific J. Math., 280:1 (2016), 227–240  mathnet  crossref  mathscinet (cited: 2)  zmath  isi (cited: 1)  elib  scopus (cited: 1)
10. Oliver Roche-Newton, Misha Rudnev, Ilya D. Shkredov, “New sum-product type estimates over finite fields”, Adv. Math., 293 (2016), 589–605  mathnet (cited: 1)  crossref  mathscinet (cited: 6)  zmath  isi (cited: 6)  elib  scopus (cited: 6)
11. 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
12. 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: 1)  elib  elib  scopus
13. 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: 4)  elib  elib  scopus (cited: 2)
14. I. D. Shkredov, “Erratum to: On some problems of Euclidean Ramsey theory”, Anal. Math., 42:3 (2016), 295  mathnet  crossref  isi  scopus
15. I. D. Shkredov, Some remarks on sets with small quotient set, 2016 , 14 pp., arXiv: 1603.04948v2
16. Shkredov, I. D., “Difference sets are not multiplicatively closed”, Discrete Anal., 2016, 17 , 21 pp.  mathnet  crossref
17. Esen Aksoy Yazici, Brendan Murphy, Misha Rudnev, Ilya Shkredov, “Growth estimates in positive characteristic via collisions”, Int. Math. Res. Not. IMRN, 2016 (Published online) , 39 pp.  mathnet  crossref  adsnasa
18. I.D. Shkredov, “On tripling constant of multiplicative subgroups”, Integers, 16 (2016), 75 , 9 pp.  mathnet
19. 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
20. 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
21. 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 (cited: 5)  zmath  isi (cited: 5)  elib (cited: 1)  scopus (cited: 5)
22. I. D. Shkredov, “On Sums of Szemerédi–Trotter Sets”, Proc. Steklov Inst. Math., 289 (2015), 300–309  mathnet  crossref  crossref  isi (cited: 5)  elib  elib  scopus (cited: 2)
23. 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  elib  elib  scopus
24. 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: 10)  elib  elib  scopus (cited: 6)
25. 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
26. 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 (cited: 8)  zmath  isi (cited: 3)  scopus (cited: 3)
27. I. D. Shkredov, “Sumsets in quadratic residues”, Acta Arith., 164:3 (2014), 221–243 , arXiv: 1305.4093v1  mathnet  crossref  mathscinet (cited: 5)  zmath  isi (cited: 7)  elib (cited: 3)  scopus (cited: 7)
28. I. D. Shkredov, “On exponential sums over multiplicative subgroups of medium size”, Finite Fields Appl., 30 (2014), 72–87  mathnet  crossref  mathscinet (cited: 9)  zmath  isi (cited: 12)  elib (cited: 8)  scopus (cited: 12)
29. I. Shkredov, “Energies and structure of additive sets”, Electron. J. Combin., 21:3 (2014), P3.44 , 53 pp.  mathnet  mathscinet (cited: 4)  zmath  isi  scopus (cited: 6)
30. S. V. Konyagin, I. D. Shkredov, “O norme Vinera podmnozhestv $\mathbb Z_p$ promezhutochnogo razmera”, Fundament. i prikl. matem., 19:5 (2014), 75–87  mathnet  mathscinet  zmath  elib; 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  crossref  mathscinet  zmath  elib  scopus

   2013
31. T. Schoen, I. D. Shkredov, “Higher moments of convolutions”, J. Number Theory, 133 (2013), 1693–1737  mathnet  crossref  mathscinet (cited: 17)  zmath  isi (cited: 16)  elib (cited: 15)  scopus (cited: 15)
32. I. D. Shkredov, On exponential sums over multiplicative subgroups of medium size, 2013 , 14 pp., arXiv: 1311.5726
33. I. D. Shkredov, New bounds for Heilbronn's exponential sum, 2013 , 14 pp., arXiv: 1302.3839
34. I. D. Shkredov, “Some new results on higher energies”, Trans. Moscow Math. Soc., 2013 (2013), 31–63  mathnet  crossref  mathscinet  zmath  elib  scopus (cited: 6)
35. I. D. Shkredov, “On Heilbronn's exponential sum”, Q. J. Math., 64:4 (2013), 1221–1230  mathnet  crossref  mathscinet (cited: 7)  zmath  isi (cited: 9)  elib (cited: 7)  scopus (cited: 9)
36. 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
37. I. D. Shkredov, T. Schoen, “Additive properties of multiplicative subgroups of $F_p$”, Quart. J. Math., 63:3 (2012), 713–722  mathnet  crossref  mathscinet (cited: 17)  zmath  isi (cited: 14)  elib (cited: 11)  scopus (cited: 15)
38. 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: 3)  elib (cited: 6)  elib (cited: 6)  scopus (cited: 5)
39. 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
40. 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 (cited: 4)  zmath  isi (cited: 4)  elib (cited: 3)  scopus (cited: 3)
41. I. D. Shkredov, T. Schoen, “On sumsets of convex sets”, Comb. Probab. Comput., 20 (2011), 793–798  crossref  mathscinet (cited: 16)  zmath  isi (cited: 14)  elib (cited: 16)  scopus (cited: 18)
42. 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 (cited: 5)

   2010
43. 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: 5)  elib (cited: 6)  elib (cited: 6)  scopus (cited: 6)
44. 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)
45. I. D. Shkredov, “O kriterii normalnosti Pyatetskogo-Shapiro dlya tsepnykh drobei”, Fundament. i prikl. matem., 16:6 (2010), 177–188  mathnet (cited: 1)  mathscinet (cited: 1)  elib; I. D. Shkredov, “On the Pyatetskii-Shapiro normality criterion for continued fractions”, J. Math. Sci., 182:4 (2012), 567–575  crossref  mathscinet  elib  scopus
46. 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

   2009
47. I. D. Shkredov, “On a two-dimensional analogue of Szemerédi's theorem in Abelian groups”, Izv. Math., 73:5 (2009), 1033–1075  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 2)  elib (cited: 2)  elib (cited: 2)  scopus (cited: 2)
48. I. D. Shkredov, “On sumsets of dissociated sets”, Online J. Anal. Comb., 2009, no. 4, Art. 4 , 26 pp.  mathscinet (cited: 8)  zmath
49. I. D. Shkredov, “Obratnaya teorema dlya $U^3()$-normy”, Sovremennye problemy matematiki i mekhaniki. Matematika. Dinamicheskie sistemy, v. 4, Izd-vo Mosk. un-ta, M., 2009, 55–127

   2008
50. I. D. Shkredov, “On sets of large trigonometric sums”, Izv. Math., 72:1 (2008), 149–168  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 5)  elib (cited: 5)  elib (cited: 5)  scopus (cited: 4)
51. I. D. Shkredov, “On Sets with Small Doubling Property”, Math. Notes, 84:6 (2008), 859–878  mathnet  crossref  crossref  mathscinet  isi (cited: 1)  elib  elib  scopus

   2007
52. N. G. Moshchevitin, I. D. Shkredov, “On the Multiplicative Properties Modulo $m$ of Numbers with Missing Digits”, Math. Notes, 81:3 (2007), 338–355  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus
53. I. D. Shkredov, “Examples of sets with large trigonometric sums”, Sb. Math., 198:12 (2007), 1805–1838  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 2)  elib  scopus (cited: 2)

   2006
54. I. D. Shkredov, “On a problem of Gowers”, Izv. Math., 70:2 (2006), 385–425  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 9)  elib (cited: 5)  elib (cited: 5)  scopus (cited: 6)
55. I. D. Shkredov, “Szemerédi's theorem and problems on arithmetic progressions”, Russian Math. Surveys, 61:6 (2006), 1101–1166  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 8)  elib (cited: 6)  elib (cited: 6)  scopus (cited: 6)
56. I. D. Shkredov, “Dynamical systems with low recurrence rate”, Sb. Math., 197:11 (2006), 1697–1712  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 1)  elib  elib  scopus
57. I. D. Shkredov, “On sets of large exponential sums”, Dokl. Math., 74:3 (2006), 860–864  mathnet  crossref  mathscinet  zmath  isi (cited: 2)  elib  elib  scopus (cited: 1)
58. I. D. Shkredov, “On a generalization of Szemerédi's theorem”, Proc. London Math. Soc. (3), 93:3 (2006), 723–760  crossref  mathscinet (cited: 15)  zmath  isi (cited: 15)  elib (cited: 12)  scopus (cited: 14)

   2005
59. I. D. Shkredov, “On a generalization of Szemerédi's theorem”, Dokl. Math., 72:3 (2005), 899–902  mathnet  mathscinet  zmath  isi (cited: 2)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 1)
60. I. D. Shkredov, “On a problem of Gowers”, Dokl. Math., 71:1 (2005), 46–48  mathnet  mathscinet  isi (cited: 5)  elib (cited: 1)  elib (cited: 1)  scopus

   2003
61. N. G. Moshchevitin, I. D. Shkredov, “On the Pyatetskii-Shapiro Criterion of Normality”, Math. Notes, 73:4 (2003), 539–550  mathnet  crossref  crossref  mathscinet  zmath  isi  elib (cited: 1)  scopus (cited: 1)
62. I. D. Shkredov, “Some additive problems connected with exponential functions”, Russian Math. Surveys, 58:4 (2003), 798–799  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 2)  scopus (cited: 1)

   2002
63. I. D. Shkredov, “Recurrence in Mean”, Math. Notes, 72:4 (2002), 576–582  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 5)  scopus (cited: 5)
64. I. D. Shkredov, “Recurrence of incomplete quotients of continued fractions”, Russian Math. Surveys, 57:4 (2002), 819–821  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 1)  elib (cited: 1)  scopus (cited: 1)
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