Zeta functions in higher Teichmuller theory

2022/03/29 by Mark Pollicott, Pollicott, Mark, Richard R. Sharp +1
Mathematics · #37C30 #Advanced Algebra and Geometry #Analytic Number Theory Research #Dynamical Systems (math.DS) #FOS: Mathematics #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.2203.15741

openalex publication_date 2022/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we introduce zeta functions and L-functions for discrete and faithful representations of surface groups in PSL(d, R), for d >= 3. These are natural generalizations of the wellknown classical Selberg zeta function and L-function for Fuchsian groups, corresponding to the case d=2.We show that these complex functions have meromorphic extensions to the entire complex plane C.

Related

• Meromorphic continuation of Selberg zeta functions with twists having non-expanding cusp monodromy
• The Selberg trace formula and Selberg zeta-function for cofinite Kleinian groups with finite-dimensional unitary representations
• The Selberg Trace Formula and Selberg Zeta-Function for Cofinite Kleinian Groups with Finite Dimensional Unitary Representations: Stony Brook University PhD Thesis
• Analytic properties of representation zeta functions of groups of type A₂
• Differences of the Selberg trace formula and Selberg type zeta functions\n for Hilbert modular surfaces