TY - JOUR
T1 - The zeta functions of Ruelle and Selberg for hyperbolic manifolds with cusps
AU - Gon, Yasuro
AU - Park, Jinsung
PY - 2010/3
Y1 - 2010/3
N2 - 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.
AB - 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.
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U2 - 10.1007/s00208-009-0408-7
DO - 10.1007/s00208-009-0408-7
M3 - Article
AN - SCOPUS:73249146859
SN - 0025-5831
VL - 346
SP - 719
EP - 767
JO - Mathematische Annalen
JF - Mathematische Annalen
IS - 3
ER -