{"title":"模态 $L$ 函数的二次扭曲力矩","authors":"Xiannan Li","doi":"10.1007/s00222-024-01265-1","DOIUrl":null,"url":null,"abstract":"<p>We prove an asymptotic for the second moment of quadratic twists of a modular <span>\\(L\\)</span>-function. This was previously known conditionally on GRH by the work of Soundararajan and Young (J. Eur. Math. Soc. 12(5):1097–1116, 2010).</p>","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Moments of quadratic twists of modular $L$ -functions\",\"authors\":\"Xiannan Li\",\"doi\":\"10.1007/s00222-024-01265-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We prove an asymptotic for the second moment of quadratic twists of a modular <span>\\\\(L\\\\)</span>-function. This was previously known conditionally on GRH by the work of Soundararajan and Young (J. Eur. Math. Soc. 12(5):1097–1116, 2010).</p>\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2024-05-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00222-024-01265-1\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, BIOMATERIALS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00222-024-01265-1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
引用次数: 0
摘要
我们证明了模态 \(L\)-函数二次扭曲第二矩的渐近性。这在之前由 Soundararajan 和 Young 的工作(J. Eur. Math.Math.12(5):1097-1116, 2010)。
Moments of quadratic twists of modular $L$ -functions
We prove an asymptotic for the second moment of quadratic twists of a modular \(L\)-function. This was previously known conditionally on GRH by the work of Soundararajan and Young (J. Eur. Math. Soc. 12(5):1097–1116, 2010).