{"title":"西格尔庞卡罗级数的线性关系及旋量l函数中心值的不消失性","authors":"Zhining Wei","doi":"10.5802/jtnb.1226","DOIUrl":null,"url":null,"abstract":"In this paper, we will first investigate the linear relations of a one parameter family of Siegel Poincaré series. Then we give the applications to the non-vanishing of Fourier coefficients of Siegel cusp eigenforms and the central values.","PeriodicalId":48896,"journal":{"name":"Journal De Theorie Des Nombres De Bordeaux","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2021-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Linear Relations of Siegel Poincaré Series and Non-vanishing of the Central Values of Spinor L-functions\",\"authors\":\"Zhining Wei\",\"doi\":\"10.5802/jtnb.1226\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we will first investigate the linear relations of a one parameter family of Siegel Poincaré series. Then we give the applications to the non-vanishing of Fourier coefficients of Siegel cusp eigenforms and the central values.\",\"PeriodicalId\":48896,\"journal\":{\"name\":\"Journal De Theorie Des Nombres De Bordeaux\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2021-10-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal De Theorie Des Nombres De Bordeaux\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.5802/jtnb.1226\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal De Theorie Des Nombres De Bordeaux","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.5802/jtnb.1226","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Linear Relations of Siegel Poincaré Series and Non-vanishing of the Central Values of Spinor L-functions
In this paper, we will first investigate the linear relations of a one parameter family of Siegel Poincaré series. Then we give the applications to the non-vanishing of Fourier coefficients of Siegel cusp eigenforms and the central values.
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