{"title":"Sums of coefficients of general L-functions over arithmetic progressions and applications","authors":"Dan Wang","doi":"10.1016/j.jnt.2024.06.011","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we study the asymptotic distribution of coefficients of general <em>L</em>-functions over arithmetic progressions without the Ramanujan conjecture. As an application, we consider the high mean of Fourier coefficients of holomorphic forms or Maass forms for <span><math><mi>Γ</mi><mo>=</mo><mrow><mi>SL</mi></mrow><mo>(</mo><mn>2</mn><mo>,</mo><mi>Z</mi><mo>)</mo></math></span> over arithmetic progressions, and improve the results of Jiang and Lü <span><span>[10]</span></span>. Our new results remove the restriction to prime module and improve the interval length of module <em>q</em>.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022314X24001574","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we study the asymptotic distribution of coefficients of general L-functions over arithmetic progressions without the Ramanujan conjecture. As an application, we consider the high mean of Fourier coefficients of holomorphic forms or Maass forms for over arithmetic progressions, and improve the results of Jiang and Lü [10]. Our new results remove the restriction to prime module and improve the interval length of module q.