论𝑝-adic Rankin-Selberg 𝐿 函数的额外零点

IF 0.7 4区 数学 Q2 MATHEMATICS
D. Benois, S. Horte
{"title":"论𝑝-adic Rankin-Selberg 𝐿 函数的额外零点","authors":"D. Benois, S. Horte","doi":"10.1090/spmj/1785","DOIUrl":null,"url":null,"abstract":"<p>A version of the extra-zero conjecture, formulated by the first named author, is proved for <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p\"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding=\"application/x-tex\">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-adic <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L\"> <mml:semantics> <mml:mi>L</mml:mi> <mml:annotation encoding=\"application/x-tex\">L</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-functions associated with Rankin–Selberg convolutions of modular forms of the same weight. This result provides an evidence in support of this conjecture in the <italic>noncritical</italic> case, which remained essentially unstudied.</p>","PeriodicalId":51162,"journal":{"name":"St Petersburg Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On extra zeros of 𝑝-adic Rankin–Selberg 𝐿-functions\",\"authors\":\"D. Benois, S. Horte\",\"doi\":\"10.1090/spmj/1785\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>A version of the extra-zero conjecture, formulated by the first named author, is proved for <inline-formula content-type=\\\"math/mathml\\\"> <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"p\\\"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding=\\\"application/x-tex\\\">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-adic <inline-formula content-type=\\\"math/mathml\\\"> <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper L\\\"> <mml:semantics> <mml:mi>L</mml:mi> <mml:annotation encoding=\\\"application/x-tex\\\">L</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-functions associated with Rankin–Selberg convolutions of modular forms of the same weight. This result provides an evidence in support of this conjecture in the <italic>noncritical</italic> case, which remained essentially unstudied.</p>\",\"PeriodicalId\":51162,\"journal\":{\"name\":\"St Petersburg Mathematical Journal\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-01-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"St Petersburg Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1090/spmj/1785\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"St Petersburg Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/spmj/1785","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0

摘要

第一位作者提出的 "零外猜想 "的一个版本被证明适用于与同重模态的兰金-塞尔伯格卷积相关的 p -adic L L 函数。这一结果为在非临界情况下支持这一猜想提供了证据,而这一猜想基本上仍未得到研究。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On extra zeros of 𝑝-adic Rankin–Selberg 𝐿-functions

A version of the extra-zero conjecture, formulated by the first named author, is proved for p p -adic L L -functions associated with Rankin–Selberg convolutions of modular forms of the same weight. This result provides an evidence in support of this conjecture in the noncritical case, which remained essentially unstudied.

求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
CiteScore
1.00
自引率
12.50%
发文量
52
审稿时长
>12 weeks
期刊介绍: This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信