Pair correlation of zeros of the real and imaginary parts of the Riemann zeta-function

被引：0

作者：

Gonek, Steven M. ^{[1
]}

Ki, Haseo ^{[2
,3
]}

机构：

[1] Univ Rochester, Dept Math, Rochester, NY 14627 USA

[2] Yonsei Univ, Dept Math, Seoul 03722, South Korea

[3] Korea Inst Adv Study, Seoul, South Korea

来源：

JOURNAL OF NUMBER THEORY | 2018年 / 186卷

基金：

新加坡国家研究基金会; 美国国家科学基金会;

关键词：

Riernann zeta-function; Zeros; Simple zeros; Pair correlation;

D O I：

10.1016/j.jnt.2017.10.024

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that if the Riemann Hypothesis is true for the Riemann zeta-function, zeta(s), and 0 < alpha < 1/2, then all but a finite number of the zeros of R zeta(a, it), I zeta(a + it), and similar functions are simple. We also study the pair correlation of the zeros of these functions assuming the Riemann Hypothesis is true and 0 < a <= 1/2. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：35 / 61

页数：27