Higher Selberg zeta functions
type: Item
instance of: scholarly article
title: Higher Selberg zeta functions
zbMATH Open document ID: 1060.11050
author: Nobushige Kurokawa
author: Masato Wakayama
published in: Communications in Mathematical Physics
publication date: 2004-11-11T00:00:00Z
review text: In [\textit{N. Kurokawa} and \textit{M. Wakayama}, A comparison between the sum over Selberg's zeros and Riemann's zeros. J. Ramanujan Math. Soc. 18, No. 3, 221--236 (2003; Zbl 1052.11062)] the authors introduced a new variant \(z(s)\) of the Selberg zeta function which they call higher Selberg zeta function. In the current paper they show that \(z(s)\) satisfies a functional equation as \(s\) is replaced by \(-s\). They describe the necessary Gamma factor in terms of triple sine functions. The proof relies on the trace formula.
Mathematics Subject Classification ID: 11M36
Mathematics Subject Classification ID: 33E20
zbMATH DE Number: 2114611
reviewed by: Anton Deitmar
MaRDI profile type: Publication
full work available at URL: s00220-004-1065-z
OpenAlex ID: W2063818956
DOI: 10.1007/S00220-004-1065-Z
Recommended article: Q4184933
Recommended article: Hierarchy of the Selberg zeta functions
Recommended article: Selberg zeta functions over function fields
Recommended article: Q3137234
Recommended article: Higher torsion zeta functions
Recommended article: Q4733924
Recommended article: Q4550585
Recommended article: Q3137229
Recommended article: ON THE RANKIN–SELBERG ZETA FUNCTION
Recommended article: Q3820686
description: scientific article; zbMATH DE number 2114611