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Элементарный подход к вычислению $\zeta(2n)$.
Чебышевский сборник. 2003. Т. 4. № 3. С. 106–110.
Ustinov A.
The article proposes an elementary approach to calculating the values of the Riemann zeta function at even positive points.
Rezvyakova I., Известия Российской академии наук. Серия математическая. Россия 2026 Т. 90 № 2 С. 62–137
We prove that the Epstein zeta-function corresponding to a binary positive definite quadratic form with integer coefficients has a positive proportion of its non-trivial zeros on the critical line. ...
Added: December 26, 2025
Ustinov A., Чебышевский сборник 2003 Т. 4 № 4 С. 137–152
In this article, methods of umbral calculus are used to prove the properties of Korobov polynomials. ...
Added: October 12, 2025
Ustinov A., Чебышевский сборник 2002 Т. 3 № 2 С. 107–122
This article examines the properties of generalized Stirling numbers. These numbers are closely related to the discrete analogues of Bernoulli polynomials introduced by Korobov. ...
Added: October 12, 2025
Ustinov A., Гузев М. А., Дальневосточный математический журнал 2016 Т. 16 № 1 С. 39–43
We use the number theory methods for explicit calculation of a static stress field in the system of a 1D chain harmonic oscillators. The sums defining stress field are presented in terms of Korobov polynomials for arbitrary number of oscillators and arbitrary averaging scale. ...
Added: October 9, 2025
Balkanova O., Conrey J. B., Frolenkov D., Canadian Journal of Mathematics 2025 Vol. 77 No. 3 P. 715–738
Consider the family of automorphic L-functions associated with primitive cusp forms of level one, ordered by weight k. Assuming that k tends to infinity, we prove a new approximation formula for the cubic moment of shifted L-values over this family which relates it to the fourth moment of the Riemann zeta function. More precisely, the formula includes a conjectural main ...
Added: June 23, 2025
Kalmynin A. B., Acta Arithmetica 2018 Vol. 186 No. 3 P. 201–217
We generalize the method of S. P. Zaitsev (2000) in order to prove omega-theorems for the Riemann zeta function and its derivatives in some regions near the line Re s=1. ...
Added: January 9, 2019