{"title":"Lower bounds for negative moments of \n \n \n \n ζ\n ′\n \n \n (\n ρ\n )\n \n \n $\\zeta ^{\\prime }(\\rho )$","authors":"Peng Gao, Liangyi Zhao","doi":"10.1112/mtk.12219","DOIUrl":null,"url":null,"abstract":"<p>We establish lower bounds for the discrete 2<i>k</i>th moment of the derivative of the Riemann zeta function at nontrivial zeros for all <math>\n <semantics>\n <mrow>\n <mi>k</mi>\n <mo><</mo>\n <mn>0</mn>\n </mrow>\n <annotation>$k<0$</annotation>\n </semantics></math> under the Riemann hypothesis and the assumption that all zeros of <math>\n <semantics>\n <mrow>\n <mi>ζ</mi>\n <mo>(</mo>\n <mi>s</mi>\n <mo>)</mo>\n </mrow>\n <annotation>$\\zeta (s)$</annotation>\n </semantics></math> are simple.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.12219","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematika","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/mtk.12219","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
We establish lower bounds for the discrete 2kth moment of the derivative of the Riemann zeta function at nontrivial zeros for all under the Riemann hypothesis and the assumption that all zeros of are simple.
期刊介绍：
Mathematika publishes both pure and applied mathematical articles and has done so continuously since its founding by Harold Davenport in the 1950s. The traditional emphasis has been towards the purer side of mathematics but applied mathematics and articles addressing both aspects are equally welcome. The journal is published by the London Mathematical Society, on behalf of its owner University College London, and will continue to publish research papers of the highest mathematical quality.
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