Determinants of Laplacians and a second limit formula in \(\text{GL}(3)\)
type: Item
instance of: scholarly article
title: Determinants of Laplacians and a second limit formula in \(\text{GL}(3)\)
zbMATH Open document ID: 0607.10019
DOI: 10.1215/S0012-7094-87-05519-0
author: Isaac Efrat
published in: Duke Mathematical Journal
publication date: 1987-01-01T00:00:00Z
review text: The aim of this paper is twofold. First, we consider the Eisenstein series on \(\text{GL}(3)\), twisted by an additive character, and evaluate it at \(s=3/2\). This is a rank two version of Kronecker's celebrated second limit formula, and thus involves functions which are \(\text{GL}(3)\) analogs of the absolute value of the eta and theta functions. We then proceed to use this formula in order to give a precise expression for the determinant of the Laplace operator on three dimensional flat tori. We find that this determinant, as a function on the moduli space of such tori, is a harmonic function there.
Mathematics Subject Classification ID: 11F66
Mathematics Subject Classification ID: 58J50
zbMATH DE Number: 3981262
zbMATH Keywords: Eisenstein series
zbMATH Keywords: GL(3)
zbMATH Keywords: second limit formula
zbMATH Keywords: Laplace operator
zbMATH Keywords: flat tori
zbMATH Keywords: harmonic function
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3981262