A factorization of the Selberg zeta function attached to a rank 1 space form
type: Item
instance of: scholarly article
title: A factorization of the Selberg zeta function attached to a rank 1 space form
zbMATH Open document ID: 0789.22024
DOI: 10.1007/BF02567041
author: Floyd L. Williams
published in: Manuscripta Mathematica
publication date: 1993-06-29T00:00:00Z
full work available at URL: https://eudml.org/doc/155766
review text: The purpose of this paper is to compare the Selberg zeta function for a cocompact discrete group acting on a rank 1 symmetric space with the regularized determinant of the resolvent operator. The main difficulty in this programme is the evaluation of a family of integrals which intervene in the calculations and the results. These are of the form \[ \int^ \infty_ 0t^{2n} (\text{sech}^ 2at) (b^ 2+t^ 2) (\log (b^ 2+t^ 2)-c) dt \] and it turns out that they can be evaluated in terms of standard functions, the most exotic of which is the Barnes' double-gamma function. The rest of the paper is devoted to deducing the consequences for the Selberg zeta-function, including its functional equation.
Mathematics Subject Classification ID: 22E40
Mathematics Subject Classification ID: 11F72
zbMATH DE Number: 222000
zbMATH Keywords: cocompact discrete group
zbMATH Keywords: symmetric space
zbMATH Keywords: regularized determinant
zbMATH Keywords: resolvent operator
zbMATH Keywords: Barnes' double-gamma function
zbMATH Keywords: Selberg zeta-function
zbMATH Keywords: functional equation
reviewed by: Samuel James Patterson
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 222000