Twisted second moments of the Riemann zeta-function and applications

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• 作者：Nicolas Robles^a ; ^{nicolas.robles@math.uzh.ch" class="auth_mail" title="E-mail the corresponding author} ; Arindam Roy^b ; ^{roy22@illinois.edu" class="auth_mail" title="E-mail the corresponding author} ; Alexandru Zaharescu^b ; ^c ; ^{zaharesc@illinois.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Riemann zeta-function ; Twisted second moment ; Mollifier ; Zeros on the critical line
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：1 February 2016
• 年：2016
• 卷：434
• 期：1
• 页码：271-314
• 全文大小：599 K

文摘

In order to compute a twisted second moment of the Riemann zeta-function, two different mollifiers, each being a combination of two different Dirichlet polynomials, were introduced separately by Bui, Conrey, and Young, and by Feng. In this article we introduce a mollifier which is a combination of four Dirichlet polynomials of different shapes. We provide an asymptotic result for the twisted second moment of class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X15008021&_mathId=si1.gif&_user=111111111&_pii=S0022247X15008021&_rdoc=1&_issn=0022247X&md5=f5aae7fd4d6175bd4d531ac3d2a4714e" title="Click to view the MathML source">ζ(s)class="mathContainer hidden">class="mathCode">$\zeta (s)$ for such choice of mollifier. A small increment on the percentage of zeros of the Riemann zeta-function on the critical line is given as an application of our results.