Introduction in Additive Combinatorics (a collection of papers for beginners) (Likbez.rar)

Publications (old)

[1]  Recurrence in Mean,  Mat. Zametki 72:4 (2002), 625-632;  English transl. Mathematical Notes 72:4 (2002), 576-582.
[2]   Recurrence of Incomplete Quotients of Continued Fractions Uspekhi Mat. Nauk 57:4 (2002), 189-190; English transl. Comm. Moscow Math. Soc. 57:4 (2002),   819-821. (.pdf)
[3]   Some Additive Problems Connected with Exponential Functions, Uspekhi Mat. Nauk 58:4 (2003), 165-166; English transl. Comm. Moscow Math. Soc. 58:4  (2003),789-799.
[4]   On the Piatetzki-Shapiro Normality Criterion (with N.G. Moshchevitin), Mat. Zametki 73:4 (2003), 577-589; English transl. Mathematical Notes 73:4 (2003), 539-550.
[5]   On one Problem of Gowers, Doklady of Russian Academy of Sciences 400:2 (2005),169-172; English transl. Doklady Mathematics 71:1 (2005), 46-48. (.pdf)
[6]   On a Generalization of Szemeredi’s Theorem, Doklady of Russian Academy of   Sciences 405:3 (2005), 315-319; English transl. Doklady Mathematics 72:3 (2005),899-902. (.pdf)
[7]   On the Piatetzki-Shapiro Normality Criterion for Continued Fractions, Fundamentalnaya i Prikladnaya Matematika, accepted for publication.
[8]    On one Problem of Gowers, Izvestiya of Russian Academy of Sciences 70:2 (2006),176-217; English transl. Izvestiya : Mathematics 70:2 (2006), 385-425. (.pdf)
[9]   On the multiplicative properties modulo m of numbers with missing digits (with N.G. Moshchevitin), Mat. Zametki 81:3 (2007), 385-404. English transl. Mathematical Notes 81:3-4 (2007), 338-355. (.pdf)
[10] On a Generalization of Szemeredi’s Theorem, Proceedings London Math. Soc., 93:3 (2006), 723-760. (.pdf)
[11] On Dynamical Systems with Slow Recurrence, Time, Mat. Sbornik 197:11 (2006), 143-158. English transl. Sbornik: Mathematics 197:11 (2006), 1697-1712. (.pdf)
[12] Szemeredi’s Theorem and Problems Concerning Arithmetic Progressions, Uspekhi Mat. Nauk 61:6 (2006), 111-178. English transl. Comm. Moscow Math. Soc. 61:6 (2006) 1101-1166. (.pdf)
[13] On Sets of Large Exponential Sums, Doklady of Russian Academy of Sciences 411:4 (2006),455-459; English transl. Doklady Mathematics 74:3 (2006), 860-864. (.pdf)
[14] On Sets of Large Exponential Sums, Izvestiya of Russian Academy of Sciences, 72, N 1, 161-182, 2008. (.pdf)
[15] Some Examples of Sets of Large Exponential Sums, Mat.Sbornik,198,N12, 105-140, 2007. (.pdf)
[16] On Sets with Small Doubling, Mat. Zametki, 84:6, 927-947; (.pdf)
[17] On a two-dimensional analog of Szemeredi’s Theorem in Abelian groups,    Izvestiya of Russian Academy of Sciences, 73:5 (2009), 455-505; (.pdf)
[18] On sumsets of dissociated sets, Online Journal of Analytic Combinatorics,  accepted for publication. (.pdf)
[19] On a result of J. Bourgain (with S.V. Konyagin), Izvestiya of Russian Academy of Sciences, submitted for publication.
[20] On monochromatic solutions of some nonlinear equations in Z/pZ, Mat. Zametki, submitted for publication.
[21] On some two-dimensional configurations in dense sets, submitted for publication.
[22] On an inverse theorem for U3(?)-norm, accepted for publication.