Γ-Cohomology and the Selberg Zeta Function

1994/11/18 by Ulrich Bunke, Bunke, Ulrich, Martin Olbrich +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #dg-ga #math.DG

paper · pdf · doi:10.48550/arxiv.dg-ga/9411004

21 pages, LATEX

arxiv created 1994/11/18 · openalex publication_date 1994/11/18 · arxiv updated 2009/11/30 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

Abstract

We propose a new method for studying n- and Γ-cohomology of globalizations of Harish-Chandra modules, where G=KAN is a rank one semisimple Lie group, Γ is a discrete subgroup of G and n=Lie(N). We prove a conjecture of Patterson relating the singularities of Selberg zeta functions with the Γ-cohomology of principal series representations if Γ is cocompact and torsion free.

Related

• Cohomological properties of the smooth globalization of a Harish-Chandra module
• Analysis on Symmetric and Locally Symmetric Spaces (Multiplicities, Cohomology and Zeta functions)
• Geometric zeta-functions of locally symmetric spaces
• The Selberg Trace Formula and Selberg Zeta-Function for Cofinite Kleinian Groups with Finite Dimensional Unitary Representations: Stony Brook University PhD Thesis
• Selmer complexes and the p-adic Hodge theory