Analogues of the Artin factorization formula for the automorphic scattering matrix and Selberg zeta-function associated to a Kleinian group

2007/02/01 by Joshua S. Friedman, Friedman, Joshua S.
Mathematics · #11F72 #11M36 #Advanced Algebra and Geometry #FOS: Mathematics #Graph theory and applications #Number Theory (math.NT) #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math.NT #math.SP #msc:11F72 #msc:11M36

paper · pdf · doi:10.48550/arxiv.math/0702030

To Appear in the Proceedings of the American Math Society; Second edition: corrected some mistakes

openalex publication_date 2007/02/01 · arxiv created 2007/09/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For Kleinian groups acting on hyperbolic three-space, we prove factorization formulas for both the Selberg zeta-function and the automorphic scattering matrix. We extend results of Venkov and Zograf from Fuchsian groups, to Kleinian groups, and we give a proof that is simple and extendable to more general groups.

Related

• Artin formalism for Selberg zeta functions of co-finite Kleinian groups
• Zeta functions and regularized determinants related to the Selberg trace formula
• Kleinian groups via strict hyperbolization
• A Jensen-Rohrlich type formula for the hyperbolic 3-space
• The Selberg Trace Formula and Selberg Zeta-Function for Cofinite Kleinian Groups with Finite Dimensional Unitary Representations: Stony Brook University PhD Thesis