无限协体积Hecke三角群的转移算子特征函数与自同构形式

IF 2 4区数学 Q1 MATHEMATICS Memoirs of the American Mathematical Society Pub Date : 2019-09-25 DOI:10.1090/memo/1423

R. Bruggeman, A. Pohl

{"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}

引用次数: 2

摘要

给出了无限协体积Hecke三角形群的几种自同构形式的上同调解释。然后我们利用这些解释建立了自同构形式空间、上同调空间和转移算子的本征函数空间之间的显同构。这些结果表明，无限体积赫克曲面的谱实体与其测地线流动动力学之间存在着深刻的关系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Memoirs of the American Mathematical Society 数学-数学

CiteScore

3.50

自引率

5.30%

发文量

审稿时长

>12 weeks

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.

期刊最新文献

Classification of 𝒪_{∞}-Stable 𝒞*-Algebras Angled Crested Like Water Waves with Surface Tension II: Zero Surface Tension Limit Hyperbolic Actions and 2nd Bounded Cohomology of Subgroups of 𝖮𝗎𝗍(𝖥_{𝗇}) Finite Groups Which are Almost Groups of Lie Type in Characteristic 𝐩 The Generation Problem in Thompson Group 𝐹