{"title":"无限协体积Hecke三角群的转移算子特征函数与自同构形式","authors":"R. Bruggeman, A. Pohl","doi":"10.1090/memo/1423","DOIUrl":null,"url":null,"abstract":"We develop cohomological interpretations for several types of automorphic forms for Hecke triangle groups of infinite covolume. We then use these interpretations to establish explicit isomorphisms between spaces of automorphic forms, cohomology spaces and spaces of eigenfunctions of transfer operators. These results show a deep relation between spectral entities of Hecke surfaces of infinite volume and the dynamics of their geodesic flows.","PeriodicalId":49828,"journal":{"name":"Memoirs of the American Mathematical Society","volume":" ","pages":""},"PeriodicalIF":2.0000,"publicationDate":"2019-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Eigenfunctions of Transfer Operators and Automorphic Forms for Hecke Triangle Groups of Infinite Covolume\",\"authors\":\"R. Bruggeman, A. Pohl\",\"doi\":\"10.1090/memo/1423\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We develop cohomological interpretations for several types of automorphic forms for Hecke triangle groups of infinite covolume. We then use these interpretations to establish explicit isomorphisms between spaces of automorphic forms, cohomology spaces and spaces of eigenfunctions of transfer operators. These results show a deep relation between spectral entities of Hecke surfaces of infinite volume and the dynamics of their geodesic flows.\",\"PeriodicalId\":49828,\"journal\":{\"name\":\"Memoirs of the American Mathematical Society\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":2.0000,\"publicationDate\":\"2019-09-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Memoirs of the American Mathematical Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1090/memo/1423\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Memoirs of the American Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/memo/1423","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Eigenfunctions of Transfer Operators and Automorphic Forms for Hecke Triangle Groups of Infinite Covolume
We develop cohomological interpretations for several types of automorphic forms for Hecke triangle groups of infinite covolume. We then use these interpretations to establish explicit isomorphisms between spaces of automorphic forms, cohomology spaces and spaces of eigenfunctions of transfer operators. These results show a deep relation between spectral entities of Hecke surfaces of infinite volume and the dynamics of their geodesic flows.
期刊介绍:
Memoirs of the American Mathematical Society is devoted to the publication of research in all areas of pure and applied mathematics. The Memoirs is designed particularly to publish long papers or groups of cognate papers in book form, and is under the supervision of the Editorial Committee of the AMS journal Transactions of the AMS. To be accepted by the editorial board, manuscripts must be correct, new, and significant. Further, they must be well written and of interest to a substantial number of mathematicians.