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

Yasuro Gon, Jinsung Park

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)719-767
Number of pages49
JournalMathematische Annalen
Volume346
Issue number3
DOIs
Publication statusPublished - Mar 2010

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Hyperbolic Manifold
Cusp
Riemann zeta function
Selberg Trace Formula
Selberg zeta Function
Meromorphic
Test function
Functional equation
Singularity

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

The zeta functions of Ruelle and Selberg for hyperbolic manifolds with cusps. / Gon, Yasuro; Park, Jinsung.

In: Mathematische Annalen, Vol. 346, No. 3, 03.2010, p. 719-767.

Research output: Contribution to journalArticle

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