{"title":"兰金-塞尔伯格 L 函数的迪里希勒系数指数和","authors":"Guangshi Lü, Qiang Ma","doi":"10.1007/s00605-024-01952-4","DOIUrl":null,"url":null,"abstract":"<p>We describe a new method to obtain upper bounds for exponential sums with multiplicative coefficients without the Ramanujan conjecture. We verify these hypothesis for (with mild restrictions) the Rankin–Selberg <i>L</i>-functions attached to two cuspidal automorphic representations.\n</p>","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":"50 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Exponential sums with the Dirichlet coefficients of Rankin–Selberg L-functions\",\"authors\":\"Guangshi Lü, Qiang Ma\",\"doi\":\"10.1007/s00605-024-01952-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We describe a new method to obtain upper bounds for exponential sums with multiplicative coefficients without the Ramanujan conjecture. We verify these hypothesis for (with mild restrictions) the Rankin–Selberg <i>L</i>-functions attached to two cuspidal automorphic representations.\\n</p>\",\"PeriodicalId\":18913,\"journal\":{\"name\":\"Monatshefte für Mathematik\",\"volume\":\"50 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-03-12\",\"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/s00605-024-01952-4\",\"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/s00605-024-01952-4","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
我们描述了一种无需拉马努扬猜想就能获得指数和乘法系数上限的新方法。我们（在温和的限制条件下）验证了附加于两个簕杜鹃花自动表征的兰金-塞尔伯格 L 函数的这些假设。
Exponential sums with the Dirichlet coefficients of Rankin–Selberg L-functions
We describe a new method to obtain upper bounds for exponential sums with multiplicative coefficients without the Ramanujan conjecture. We verify these hypothesis for (with mild restrictions) the Rankin–Selberg L-functions attached to two cuspidal automorphic representations.
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