Head of the Department of Number Theory at the Steklov institute, academician

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Keywords: trigonometric series, polynomials, best approximation, character sums.

In joint works with V.N. Temlyakov (link, link) S.V. Konyagin obtained necessary and sufficient conditions on greedy approximations both in general Banach space and in classical case of trigonometric system and spaces \(L_p\), \(p \neq 2\). In work (link) they introduced the notion of greedy basis and democratic basis. These notions became in demand among the specialists; the work has been cited 262 times (according to Google Scholar). In the work (link) with coauthors he has constructed explicit examples of RIP-matrices in a new range of parameters and, thus, obtained the improvement in the problem formulated by Terence Tao.

### Publications (recent):

*2023*

→ B. Kashin, S. Konyagin, V. Temlyakov, "Sampling discretization of the uniform norm", Constr. Approx., 57 (2023), 663–694, DOI, arXiv.

→ M. G. Grigoryan, S. V. Konyagin, "On Fourier series in the multiple trigonometric system", Uspekhi Mat. Nauk, 78:4(472) (2023), 201–202, DOI.

→ S. Konyagin, P. Pollack, "A problem in comparative order theory", Period. Math. Hung., 86:1 (2023), 24–36, DOI, arXiv.

→ H. L. Fleischmann, S. V. Konyagin, S. J. Miller, E. A. Palsson, E. Pesikoff, C. Wolf, "Distinct angles in general position", Discrete Math., 346:4 (2023), 113283, DOI, arXiv.

→ M. R. Gabdullin, S. V. Konyagin, V. V. Iudelevich, "Karatsuba's divisor problem and related questions", Mat. Sb., 214:7 (2023), 27–41, DOI.

→ R. Dietmann, C. Elsholtz, A. Kalmynin, S. Konyagin, J. Maynard, "Longer gaps between values of binary quadratic forms", Int. Math. Res. Not. IMRN, 2023:12 (2023), 10313–10349, DOI.

*2022*

→ S. V. Konyagin, M. A. Korolev, "On Titchmarsh's Phenomenon in the Theory of the Riemann Zeta Function", Approximation Theory, Functional Analysis, and Applications. Collected papers. On the occasion of the 70th birthday of Academician B. S. Kashin. Trudy MIAN, 319 (2022), 169–188, DOI.

→ S. V. Konyagin, "O skhodimosti podposledovatelnosti chastnykh summ trigonometricheskogo ryada Fure po Pringskheimu", Trudy IMM UrO RAN, 28:4 (2022), 121–127, DOI.

→ S. V. Konyagin, I. E. Shparlinski, I. V. Vyugin, "Polynomial Equations in Subgroups and Applications", Analysis at Large, Dedicated to the Life and Work of Jean Bourgain, eds. A. Avila, M. Th. Rassias, Y. Sinai, Springer, 2022, 273–297, DOI, arXiv.

→ S. Konyagin, P. Pollack, "A problem in comparative order theory", Period. Math. Hung., 2022, 1–12, DOI, arXiv.

→ S. Konyagin, H. Queffélec, E. Saksman, K. Seip, "Riesz projection and bounded mean oscillation for Dirichlet series", Studia Math., 262:2 (2022), 121–149, DOI.

*2021*

→ S. V. Konyagin, "On Irregularity of Finite Sequences", Analytic and Combinatorial Number Theory, Collected papers. In commemoration of the 130th birth anniversary of Academician Ivan Matveevich Vinogradov, Proc. Steklov Inst. Math., 314 (2021), 90–95, DOI.

→ D. V. Treschev, S. V. Konyagin, V. N. Chubarikov, M. A. Korolev, M. R. Gabdullin, "Analytic and Combinatorial Number Theory, Collected papers. In commemoration of the 130th birth anniversary of Academician Ivan Matveevich Vinogradov", Proc. Steklov Inst. Math., 314 (2021), 346 p., DOI (book).

→ P. A. Borodin, S. V. Konyagin, "Projection Greedy Algorithm", Math. Notes, 110:1 (2021), 16–25, DOI.

→ K. Ford, S. Konyagin, J. Maynard, S. V. Pomerance, T. Tao, "Long gaps in sieved sets", J. Eur. Math. Soc. (JEMS), 23:2 (2021), 667–700, DOI, arXiv.

→ K. Ford, S. Konyagin, "Divisibillity of the certain binomial coefficient \({2n}\choose{n}\)", Transactions of the American Mathematical Society, 374:2 (2021), 923–953, DOI, arXiv.

*2020*

→ S. Konyagin, B. Sudakov, "An extremal problem for integer sparse recovery", Linear Algebra Appl., 56:1 (2020), 1–6, DOI, arXiv.

→ S. V. Konyagin, E. Shaparlinski, I. V. Vyugin, "Polynomial equations in subgroups and applications", arXiv.

→ S. Konyagin, H. Queffelec, E. Saksman, K. Seip, "Riesz projection and bounded mean oscillation for Dirichlet series", arXiv.

→ S. V. Konyagin, S. V. Makarychev, I. E. Shparlinski, I. V. Vyugin, "On the structure of graphs of Markoff triples", Q. J. Math., 72:2 (2020), 637–648, DOI.

→ S. V. Konyagin, "On Zeros of Sums of Cosines", Math. Notes, 108:4 (2020), 538–541, DOI.

→ K. Ford, S. Konyagin, "Gaps between totients", arXiv.

→ 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, DOI.

→ M. R. Gabdullin, S. V. Konyagin, "Stechkin’s works in number theory", Chebyshevskii Sb., 21:4 (2020), 9–18, DOI.

→ 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, DOI.

*2018*

→ K. Ford, B. Green, S. Konyagin, J. Maynard, T. Tao, "Long gaps between primes", J. Amer. Math. Soc., 31:1 (2018), 65–105, DOI, arXiv.

→ S. V. Konyagin, I. D. Shkredov, "On subgraphs of random Cayley sum graphs", European J. Combin., 70 (2018), 61–74, DOI, arXiv.

→ С. В. Konyagin, A. A. Kuleshov, V. E. Maiorov, "Some Problems in the Theory of Ridge Functions", Proc. Steklov Inst. Math., 301 (2018), 144–169, DOI.

→ 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, DOI.

→ S. V. Konyagin, "On the Recovery of an Integer Vector from Linear Measurements", Math. Notes, 104:6 (2018), 859–865, DOI.

*2017*

→ S. V. Konyagin, M. A. Korolev, "Irreducible solutions of an equation involving reciprocals", Sb. Math., 208:12 (2017), 1818–1834, DOI.

→ K. Ford, M. Z. Garaev, S. V. Konyagin, "On the smallest simultaneous power nonresidue modulo a prime", Forum Math., 29:2 (2017), 347–355, DOI.