{"title":"将公式和应用程序跟踪到类号","authors":"N. Raulf","doi":"10.2478/s11533-013-0384-8","DOIUrl":null,"url":null,"abstract":"In this paper we compute the trace formula for Hecke operators acting on automorphic forms on the hyperbolic 3-space for the group PSL2($\\mathcal{O}_K $) with $\\mathcal{O}_K $ being the ring of integers of an imaginary quadratic number field K of class number HK > 1. Furthermore, as a corollary we obtain an asymptotic result for class numbers of binary quadratic forms.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"34 1","pages":"824-847"},"PeriodicalIF":0.0000,"publicationDate":"2014-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Trace formulae and applications to class numbers\",\"authors\":\"N. Raulf\",\"doi\":\"10.2478/s11533-013-0384-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we compute the trace formula for Hecke operators acting on automorphic forms on the hyperbolic 3-space for the group PSL2($\\\\mathcal{O}_K $) with $\\\\mathcal{O}_K $ being the ring of integers of an imaginary quadratic number field K of class number HK > 1. Furthermore, as a corollary we obtain an asymptotic result for class numbers of binary quadratic forms.\",\"PeriodicalId\":50988,\"journal\":{\"name\":\"Central European Journal of Mathematics\",\"volume\":\"34 1\",\"pages\":\"824-847\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2014-03-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Central European Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2478/s11533-013-0384-8\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Central European Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2478/s11533-013-0384-8","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In this paper we compute the trace formula for Hecke operators acting on automorphic forms on the hyperbolic 3-space for the group PSL2($\mathcal{O}_K $) with $\mathcal{O}_K $ being the ring of integers of an imaginary quadratic number field K of class number HK > 1. Furthermore, as a corollary we obtain an asymptotic result for class numbers of binary quadratic forms.
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