Zur Berechnung des Ranges der Schar der elliptischen Spitzenformen. (On the calculation of the dimension of the vector space of elliptic cusp forms)
type: Item
instance of: scholarly article
title: Zur Berechnung des Ranges der Schar der elliptischen Spitzenformen. (On the calculation of the dimension of the vector space of elliptic cusp forms)
zbMATH Open document ID: 0707.11034
DOI: 10.1007/BF02942316
published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
publication date: 1989-01-01T00:00:00Z
review text: Let \(\eta\) (q,g) denote the dimension of the vector space of elliptic cusp forms of integral weight g for the principal congruence subgroup of level q. The author applies the Selberg trace formula in order to compute \(\eta\) (q,g) including the cases \(g=1\) and \(g=2\). It is remarkable that, contrary to the case \(g\geq 3\), the hyperbolic elements give a contribution to the dimension integral if \(g=1,2\). The basic step is to derive the meromorphic continuation of the logarithmic derivative of a Selberg zeta function.
Mathematics Subject Classification ID: 11F11
Mathematics Subject Classification ID: 11F72
zbMATH DE Number: 4160843
zbMATH Keywords: elliptic cusp forms
zbMATH Keywords: Selberg trace formula
zbMATH Keywords: dimension integral
zbMATH Keywords: Selberg zeta function
author: Ulrich Christian
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4160843