The zeta functions of Ruelle and Selberg for hyperbolic manifolds with cusps

Yasuro Gon, Jinsung Park

研究成果: Contribution to journalArticle査読

13 被引用数 (Scopus)

抄録

In this paper, we study the Ruelle zeta function and the Selberg zeta functions attached to the fundamental representations for real hyperbolic manifolds with cusps. In particular, we show that they have meromorphic extensions to ℂ and satisfy functional equations. We also derive the order of the singularity of the Ruelle zeta function at the origin. To prove these results, we completely analyze the weighted unipotent orbital integrals on the geometric side of the Selberg trace formula when test functions are defined for the fundamental representations.

本文言語英語
ページ(範囲)719-767
ページ数49
ジャーナルMathematische Annalen
346
3
DOI
出版ステータス出版済み - 3 2010

All Science Journal Classification (ASJC) codes

  • 数学 (全般)

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