Multiple sine functions and Selberg zeta functions
type: Item
instance of: scholarly article
title: Multiple sine functions and Selberg zeta functions
zbMATH Open document ID: 0738.11041
author: Nobushige Kurokawa
published in: Proceedings of the Japan Academy. Series A
publication date: 1992-06-27T00:00:00Z
review text: Forming suitable Weierstraß products the author defines a multiple gamma function \(G_ r\) (related to the Barnes multiple gamma function) and a multiple sine function \(F_ r\) of order \(r\geq 2\). The multiple sine functions are related with the polylogarithm function \(Li_ k(x)\) and may be used to express special values of zeta functions such as \(\zeta(2m+1)\) (\(m\geq 1\)). The main result is an announcement of the calculation of the gamma factors involved in the Selberg-Gangolli- Wakayama zeta functions of rank one locally symmetric spaces. A typical example is the case of an even dimensional real hyperbolic space.
Mathematics Subject Classification ID: 11F72
Mathematics Subject Classification ID: 11M41
Mathematics Subject Classification ID: 58J52
Mathematics Subject Classification ID: 11M06
zbMATH DE Number: 29817
zbMATH Keywords: multiple gamma function
zbMATH Keywords: multiple sine functions
zbMATH Keywords: polylogarithm function
zbMATH Keywords: Selberg-Gangolli-Wakayama zeta functions
zbMATH Keywords: symmetric spaces
zbMATH Keywords: hyperbolic space
reviewed by: Jürgen Elstrodt
MaRDI profile type: Publication
full work available at URL: pjaa.67.61
OpenAlex ID: W2061922573
cites work: Q3797272
cites work: Zeta functions of Selberg's type for compact space forms of symmetric spaces of rank one
cites work: Parabolic components of zeta functions
cites work: Q4733924
cites work: Q3137235
cites work: Q3237356
cites work: Q4138810
cites work: Q4184934
cites work: Zeta functions of Selberg's type associated with homogeneous vector bundles
DOI: 10.3792/PJAA.67.61
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description: scientific article; zbMATH DE number 29817