Eisenstein series and Cartan groups
type: Item
instance of: scholarly article
title: Eisenstein series and Cartan groups
zbMATH Open document ID: 0607.10018
author: Isaac Efrat
published in: Illinois Journal of Mathematics
publication date: 1987-01-01T00:00:00Z
review text: The principal congruence subgroup \(\Gamma\) (N) has an Eisenstein series associated to it at each cusp, which admits a Fourier expansion at each other cusp. This results in a matrix, whose determinant plays a key role in the theory, mostly due to its appearance in the trace formula. This paper introduces C(N), the Cartan subgroup of \(GL_ 2({\mathbb{Z}}/N {\mathbb{Z}})\) into the study of these Eisenstein series, and to use it in order to give a precise formula for this determinant. Our main theorem shows that it can be naturally expressed in terms of L-functions on C(N).
Mathematics Subject Classification ID: 11F27
Mathematics Subject Classification ID: 11F70
Mathematics Subject Classification ID: 11F06
Mathematics Subject Classification ID: 11F67
Mathematics Subject Classification ID: 22E40
zbMATH DE Number: 3981261
zbMATH Keywords: trace formula
zbMATH Keywords: Cartan subgroup
zbMATH Keywords: Eisenstein series
zbMATH Keywords: L-functions
MaRDI profile type: Publication
Recommended article: Eisenstein Series on Kähler's Poincaré Group
Recommended article: Eisenstein series on loop groups
Recommended article: Eisenstein series and quantum groups
Recommended article: On Eisenstein series and the cohomology of arithmetic groups
Recommended article: Q3764214
Recommended article: Cusps, Kleinian groups, and Eisenstein series
Recommended article: On the Eisenstein series of Hilbert modular groups
Recommended article: Eisenstein integers and related \(C\)-groups
Recommended article: Eisenstein series on arithmetic quotients of loop groups
Recommended article: Eisenstein series and cohomology of arithmetic groups: The generic case
description: scientific article; zbMATH DE number 3981261