Observations on Hecke eigenforms on the Hecke groups \(G(\sqrt{2})\) and \(G(\sqrt{3})\)
type: Item
instance of: scholarly article
title: Observations on Hecke eigenforms on the Hecke groups \(G(\sqrt{2})\) and \(G(\sqrt{3})\)
zbMATH Open document ID: 0565.10022
DOI: 10.1007/BF02941489
author: Günter Köhler
published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
publication date: 1985-01-01T00:00:00Z
review text: For \(N=2\) or 3, the Hecke group \(G(\sqrt{N})\) is generated by the transformations \(z\to z+\sqrt{N}\) and \(z\to -1/z\). The paper contains: (1) Some identities for divisor sums which come from identities among the Eisenstein series on \(G(\sqrt{2})\) and \(G(\sqrt{3})\). (2) Congruences and identities for the coefficients of the discriminant forms of weight 8 on \(G(\sqrt{2})\) resp. of weight 6 on \(G(\sqrt{3})\). (3) Many congruences and sharp estimates for the coefficients of Hecke's modular forms of real nebentypus and weights \(k\equiv 1\pmod 6\) on \(\Gamma^*(3)\) (or, equivalently, on the conjugate group \(G(\sqrt{3}))\) which follow in an elementary way from the definition of these forms by means of theta series with grössencharacter associated to the integers in \({\mathbb Q}(\sqrt{-3})\).
reviewed by: Günter Köhler
Mathematics Subject Classification ID: 11F11
zbMATH DE Number: 3900860
zbMATH Keywords: Hecke group
zbMATH Keywords: identities for divisor sums
zbMATH Keywords: Eisenstein series
zbMATH Keywords: congruences
zbMATH Keywords: identities
zbMATH Keywords: discriminant forms
zbMATH Keywords: Hecke's modular forms of real nebentypus
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02941489
OpenAlex ID: W2082911080
description: scientific article; zbMATH DE number 3900860