{"title":"半积分权的非全纯质量形式的Voronoi求和公式","authors":"Olga Balkanova, Dmitry Frolenkov","doi":"10.1007/s00605-023-01921-3","DOIUrl":null,"url":null,"abstract":"<p>We prove a Voronoi summation formula for non-holomorphic half-integral weight Maass forms on <span>\\(\\Gamma _0(4)\\)</span> without any restrictions on the denominator of a fraction in the exponential function. As an application we obtain a Voronoi summation formula for the values of Zagier <i>L</i>-series.\n</p>","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":"61 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Voronoi summation formula for non-holomorphic Maass forms of half-integral weight\",\"authors\":\"Olga Balkanova, Dmitry Frolenkov\",\"doi\":\"10.1007/s00605-023-01921-3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We prove a Voronoi summation formula for non-holomorphic half-integral weight Maass forms on <span>\\\\(\\\\Gamma _0(4)\\\\)</span> without any restrictions on the denominator of a fraction in the exponential function. As an application we obtain a Voronoi summation formula for the values of Zagier <i>L</i>-series.\\n</p>\",\"PeriodicalId\":18913,\"journal\":{\"name\":\"Monatshefte für Mathematik\",\"volume\":\"61 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-11-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Monatshefte für Mathematik\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s00605-023-01921-3\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Monatshefte für Mathematik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s00605-023-01921-3","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
本文证明了\(\Gamma _0(4)\)上非全纯半积分权质量形式的Voronoi求和公式，该公式对指数函数中分数的分母没有任何限制。作为应用，我们得到了Zagier l -级数值的Voronoi求和公式。
A Voronoi summation formula for non-holomorphic Maass forms of half-integral weight
We prove a Voronoi summation formula for non-holomorphic half-integral weight Maass forms on \(\Gamma _0(4)\) without any restrictions on the denominator of a fraction in the exponential function. As an application we obtain a Voronoi summation formula for the values of Zagier L-series.
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