MathematikaPub Date : 2023-08-10DOI: 10.1112/mtk.12219
Peng Gao, Liangyi Zhao
{"title":"Lower bounds for negative moments of \u0000 \u0000 \u0000 \u0000 ζ\u0000 ′\u0000 \u0000 \u0000 (\u0000 ρ\u0000 )\u0000 \u0000 \u0000 $zeta ^{prime }(rho )$","authors":"Peng Gao, Liangyi Zhao","doi":"10.1112/mtk.12219","DOIUrl":"10.1112/mtk.12219","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>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 <mo><</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$k<0$</annotation>\u0000 </semantics></math> under the Riemann hypothesis and the assumption that all zeros of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>ζ</mi>\u0000 <mo>(</mo>\u0000 <mi>s</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$zeta (s)$</annotation>\u0000 </semantics></math> are simple.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"69 4","pages":"1081-1103"},"PeriodicalIF":0.8,"publicationDate":"2023-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.12219","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42508800","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}