Universality of the Riemann zeta-function in short intervals

被引：19

作者：

Laurincikas, Antanas ^{[1
]}

机构：

[1] Vilnius Univ, Fac Math & Informat, Inst Math, Naugarduko Str 24, LT-03225 Vilnius, Lithuania

来源：

JOURNAL OF NUMBER THEORY | 2019年 / 204卷

关键词：

Mergelyan theorem; Riemann zeta-function; Universality; Weak convergence; VALUES;

D O I：

10.1016/j.jnt.2019.04.006

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

By the Voronin theorem, the set of shifts of the Riemann zeta-function zeta(s+i tau), s = sigma + it, tau is an element of R, that approximate any given non-vanishing analytic function defined on {s is an element of C : 1/2 < sigma < 1} has a positive lower density. In the paper, it is proved that the same property of the above shifts remains valid in the intervals [T,T + H] with T-1/3(log T)(26/15) <= H <= T. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：279 / 295

页数：17

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