Computation of Weng's rank 2 zeta function over an algebraic number field
type: Item
instance of: scholarly article
title: Computation of Weng's rank 2 zeta function over an algebraic number field
zbMATH Open document ID: 1135.11061
author: Tsukasa Hayashi
published in: Journal of Number Theory
publication date: 2007-09-13T00:00:00Z
review text: Weng's rank \(r\) non-abelian zeta-function \(\xi_{F,r}\) of an algebraic number field \(F\) is represented as an integral of the Eisenstein series over the moduli space of the semistable \(O_F\)-lattices with rank \(r\). The author proves that \[ \xi_{F,2}(s)=C_0\left(\frac{\widehat{\zeta_F}(2s)}{s-1}-\frac{\widehat{\zeta_F}(2s-1)}{s}\right), \] where \( \widehat{\zeta_F}(s)\) is the completed Dedekind zeta function of \(F\) and \(C_0\) is a non-zero constant. Moreover, \(\xi_{F,2}(s)\) has all its zeros on the critical line \(\Re(s)=\frac12.\)
reviewed by: Florin Nicolae
Mathematics Subject Classification ID: 11R42
Mathematics Subject Classification ID: 11M41
zbMATH DE Number: 5190754
zbMATH Keywords: non-abelian zeta function
zbMATH Keywords: semi-stable lattice
zbMATH Keywords: Eisenstein series
MaRDI profile type: Publication
full work available at URL: j.jnt.2006.12.007
OpenAlex ID: W2040139038
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DOI: 10.1016/J.JNT.2006.12.007
description: scientific article; zbMATH DE number 5190754