On a Linear Form in the Ordinates of Zeros of the Riemann Zeta Function

IF 0.6 4区数学 Q3 MATHEMATICS

Mathematical Notes Pub Date : 2024-04-22 DOI:10.1134/s0001434624010103

E. D. Yudelevich

引用次数: 0

Abstract

We obtain an asymptotic formula for the sum

$$H=\sum_{0<\gamma_k\le T,\,1\le k\le 4}h(\gamma_1+\gamma_2-\gamma_3-\gamma_4),$$

where the $\gamma_k$ run over the imaginary parts of nontrivial zeros of the Riemann zeta function with multiplicities taken into account and the function $h$ belongs to some special class of functions in $L^1(\mathbb R)$.

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论黎曼 Zeta 函数零点序列中的线性形式

摘要我们得到了总和 $$H=\sum_{0<；\h(\gamma_1+\gamma_2-\gamma_3-\gamma_4)、$$ 其中$\gamma_k$遍历黎曼zeta函数的非微不足道的零点的虚部，并将乘数考虑在内，函数$h$属于$L^1(\mathbb R)$中的某类特殊函数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Notes 数学-数学

CiteScore

0.90

自引率

16.70%

发文量

179

审稿时长

24 months

期刊介绍： Mathematical Notes is a journal that publishes research papers and review articles in modern algebra, geometry and number theory, functional analysis, logic, set and measure theory, topology, probability and stochastics, differential and noncommutative geometry, operator and group theory, asymptotic and approximation methods, mathematical finance, linear and nonlinear equations, ergodic and spectral theory, operator algebras, and other related theoretical fields. It also presents rigorous results in mathematical physics.