短区间内黎曼函数的联合离散通用性

IF 1.6 3区数学 Q1 MATHEMATICS Mathematical Modelling and Analysis Pub Date : 2023-10-20 DOI:10.3846/mma.2023.18884

Kalyan Chakraborty, Shigeru Kanemitsu, Antanas Laurinčikas

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引用次数: 1

摘要

本文证明了在上定义的近似解析非消失函数f1(s)，…，fr(s)的黎曼ζ函数的离散位移集在区间[N,N + M]内具有正密度，且具有实数a1，…，在q上线性无关，对于某些绝对收敛的Dirichlet级数的移位也得到了类似的结果。

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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ON JOINT DISCRETE UNIVERSALITY OF THE RIEMANN ZETA-FUNCTION IN SHORT INTERVALS

In the paper, we prove that the set of discrete shifts of the Riemann zeta-function approximating analytic nonvanishing functions f1(s),...,fr(s) defined on has a positive density in the interval [N,N + M] with with real algebraic numbers a1,...,ar linearly independent over Q. A similar result is obtained for shifts of certain absolutely convergent Dirichlet series.

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