广义软化子在黎曼ζ函数中的应用

Pub Date : 2018-01-01 DOI:10.2206/KYUSHUJM.72.35

Keiju Sono

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引用次数: 5

摘要

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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AN APPLICATION OF GENERALIZED MOLLIFIERS TO THE RIEMANN ZETA-FUNCTION

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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