On the zeros of Riemann's zeta-function on the critical line

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• 作者：Siegfred Alan C. Baluyot¹ ; ^{sbaluyot@ur.rochester.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：11M06 ; 11M26
• 刊名：Journal of Number Theory
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：165
• 期：Complete
• 页码：203-269
• 全文大小：874 K

文摘

We combine the mollifier method with a zero detection method of Atkinson to prove in a new way that a positive proportion of the nontrivial zeros of the Riemann zeta-function 16000895&_mathId=si1.gif&_user=111111111&_pii=S0022314X16000895&_rdoc=1&_issn=0022314X&md5=68e6d6ed367871fb848bebd39027b87a" title="Click to view the MathML source">ζ(s)$\zeta (s)$ are on the critical line. One of the main ingredients of the proof is an estimate for a mollified fourth moment of 16000895&_mathId=si1.gif&_user=111111111&_pii=S0022314X16000895&_rdoc=1&_issn=0022314X&md5=68e6d6ed367871fb848bebd39027b87a" title="Click to view the MathML source">ζ(s)$\zeta (s)$. We deduce this estimate from the twisted fourth moment formula that has been recently developed by Hughes and Young.