{"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":"20 1","pages":""},"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\":\"20 1\",\"pages\":\"\"},\"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。
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 pp-adic LL-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.
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.
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