Eigenfunctions of Transfer Operators and Automorphic Forms for Hecke Triangle Groups of Infinite Covolume

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

引用次数: 2

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.

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无限协体积Hecke三角群的转移算子特征函数与自同构形式

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。

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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.

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