AN APPLICATION OF GENERALIZED MOLLIFIERS TO THE RIEMANN ZETA-FUNCTION

IF 0.6 4区数学 Q3 MATHEMATICS

Kyushu Journal of Mathematics Pub Date : 2018-01-01 DOI:10.2206/KYUSHUJM.72.35

Keiju Sono

引用次数: 5

Abstract

In this paper, we establish the asymptotic formula for the second moment of the Riemann zeta-function twisted by a (3+ 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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广义软化子在黎曼ζ函数中的应用

本文建立了由(3+ 1)片柔子扭转的Riemann ζ函数二阶矩的渐近公式，该柔子是对Bui, Conrey和Young [Acta. j]所考虑的两片柔子的推广。数学学报，150(1)(2011)，35-64。作为一个应用，我们得到了黎曼函数的临界零的比例的下界。

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

Kyushu Journal of Mathematics 数学-数学

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Kyushu Journal of Mathematics is an academic journal in mathematics, published by the Faculty of Mathematics at Kyushu University since 1941. It publishes selected research papers in pure and applied mathematics. One volume, published each year, consists of two issues, approximately 20 articles and 400 pages in total. More than 500 copies of the journal are distributed through exchange contracts between mathematical journals, and available at many universities, institutes and libraries around the world. The on-line version of the journal is published at "Jstage" (an aggregator for e-journals), where all the articles published by the journal since 1995 are accessible freely through the Internet.