{"title":"AN APPLICATION OF GENERALIZED MOLLIFIERS TO THE RIEMANN ZETA-FUNCTION","authors":"Keiju Sono","doi":"10.2206/KYUSHUJM.72.35","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":49929,"journal":{"name":"Kyushu Journal of Mathematics","volume":"7 1","pages":"35-69"},"PeriodicalIF":0.6000,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2206/KYUSHUJM.72.35","citationCount":"5","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Kyushu Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2206/KYUSHUJM.72.35","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 5
Abstract
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.
期刊介绍：
The Kyushu Journal of Mathematics is an academic journal in mathematics, published by the Faculty of Mathematics at Kyushu University since 1941. It publishes selected research papers in pure and applied mathematics. One volume, published each year, consists of two issues, approximately 20 articles and 400 pages in total.
More than 500 copies of the journal are distributed through exchange contracts between mathematical journals, and available at many universities, institutes and libraries around the world. The on-line version of the journal is published at "Jstage" (an aggregator for e-journals), where all the articles published by the journal since 1995 are accessible freely through the Internet.
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