Addendum to ``On the scattering matrix of elliptic modular groups''
type: Item
instance of: scholarly article
title: Addendum to ``On the scattering matrix of elliptic modular groups''
zbMATH Open document ID: 0770.11027
DOI: 10.1215/S0012-7094-91-06421-5
author: Ulrich Christian
published in: Duke Mathematical Journal
publication date: 1992-09-27T00:00:00Z
review text: The author estimates the number of poles in the region \(0\leq\text{Re}(s)<{1\over 2}\), \(0<\text{Im}(s)\leq T\) of the determinant of the scattering matrix associated with the nonholomorphic Eisenstein series of weight \(g\) for the principal congruence subgroup of level \(q\) of the elliptic modular group. The asymptotic result is \[ {p(q)\over\pi}T\log T+c(q,g)T+O(\log T)\quad (T\to\infty) \] with certain constants \(p(q)\) and \(c(q,g)\). This improves his earlier result [Duke Math. J. 62, 479-509 (1991; Zbl 0729.11026)], where the error term was \(O(T)\).
Mathematics Subject Classification ID: 11F72
Mathematics Subject Classification ID: 11F37
zbMATH DE Number: 58555
zbMATH Keywords: number of poles
zbMATH Keywords: scattering matrix
zbMATH Keywords: nonholomorphic Eisenstein series
zbMATH Keywords: principal congruence subgroup
zbMATH Keywords: elliptic modular group
zbMATH Keywords: asymptotic result
reviewed by: Aloys Krieg
MaRDI profile type: Publication
cites work: Über die Scatteringmatrix elliptischer Modulgruppen. (On the scattering matrix of elliptic modular groups)
cites work: Q3900124
cites work: Eisenstein series and Cartan groups
cites work: Q3216732
description: scientific article; zbMATH DE number 58555