AN APPLICATION OF GENERALIZED MOLLIFIERS TO THE RIEMANN ZETA-FUNCTION

被引：4

作者：

Sono, Keiju ^{[1
]}

机构：

[1] Ehime Univ, Matsuyama, Ehime, Japan

来源：

KYUSHU JOURNAL OF MATHEMATICS | 2018年 / 72卷 / 01期

基金：

日本学术振兴会;

关键词：

Riemann zeta-function; mollifier method; critical zeros; ZEROS;

D O I：

10.2206/kyushujm.72.35

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we establish the asymptotic formula for the second moment of the Riemann zeta-function twisted by a (Lambda + 1)-piece mollifier which is a generalization of the two-piece mollifier considered by Bui, Conrey and Young [Acta. Arith. 150(1) (2011), 35-64]. As an application, we obtain a lower bound for the proportion of critical zeros of the Riemann zeta-function.

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页码：35 / 69

页数：35

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