Hecke-Maass L 函数谱平均的无零区

IF 0.6 3区数学 Q3 MATHEMATICS

Acta Mathematica Hungarica Pub Date : 2024-05-09 DOI:10.1007/s10474-024-01430-1

E. M. Sandeep

{"title":"Hecke-Maass L 函数谱平均的无零区","authors":"E. M. Sandeep","doi":"10.1007/s10474-024-01430-1","DOIUrl":null,"url":null,"abstract":"We provide a non-vanishing region for an infinite sum of weight zero Hecke–Maass L-functions for the full modular group inside the critical strip. For given positive parameters T and \\(1 \\leq M \\ll \\frac{T}{\\log T}\\), T large, we also count the number of Hecke–Maass cusp forms whose L-values are non-zero at any point s in this region and whose spectral parameters \\(t_j\\) lie in short intervals.","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Zero free region for spectral averages of Hecke–Maass L-functions\",\"authors\":\"E. M. Sandeep\",\"doi\":\"10.1007/s10474-024-01430-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We provide a non-vanishing region for an infinite sum of weight zero Hecke–Maass L-functions for the full modular group inside the critical strip. For given positive parameters T and \\\\(1 \\\\leq M \\\\ll \\\\frac{T}{\\\\log T}\\\\), T large, we also count the number of Hecke–Maass cusp forms whose L-values are non-zero at any point s in this region and whose spectral parameters \\\\(t_j\\\\) lie in short intervals.\",\"PeriodicalId\":50894,\"journal\":{\"name\":\"Acta Mathematica Hungarica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-05-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Mathematica Hungarica\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10474-024-01430-1\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Hungarica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10474-024-01430-1","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

我们为临界带内的全模态群的零权 Hecke-Maass L 函数的无限和提供了一个非求和区域。对于给定的正参数 T 和 \(1 \leq M \ll \frac{T}\{log T}\), T 大，我们还计算了在该区域内任意点 s 的 L 值都非零并且其谱参数 \(t_j\) 位于短区间内的 Hecke-Maass cusp 形式的数量。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Zero free region for spectral averages of Hecke–Maass L-functions

We provide a non-vanishing region for an infinite sum of weight zero Hecke–Maass L-functions for the full modular group inside the critical strip. For given positive parameters T and \(1 \leq M \ll \frac{T}{\log T}\), T large, we also count the number of Hecke–Maass cusp forms whose L-values are non-zero at any point s in this region and whose spectral parameters \(t_j\) lie in short intervals.

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

Acta Mathematica Hungarica 数学-数学

CiteScore

1.50

自引率

11.10%

发文量

审稿时长

4-8 weeks

期刊介绍： Acta Mathematica Hungarica is devoted to publishing research articles of top quality in all areas of pure and applied mathematics as well as in theoretical computer science. The journal is published yearly in three volumes (two issues per volume, in total 6 issues) in both print and electronic formats. Acta Mathematica Hungarica (formerly Acta Mathematica Academiae Scientiarum Hungaricae) was founded in 1950 by the Hungarian Academy of Sciences.