Hecke operators on modular forms of half-integral weight
type: Item
instance of: scholarly article
title: Hecke operators on modular forms of half-integral weight
zbMATH Open document ID: 0638.10021
DOI: 10.1007/BF01194024
author: B. Ramakrishnan
author: T. C. Vasudevan
author: M. Manickam
published in: Archiv der Mathematik
publication date: 1988-01-01T00:00:00Z
review text: In the paper [Arch. Math. 32, 158-165 (1979; Zbl 0407.10022)] \textit{Hong- Jen Hsiao} and \textit{Hong-Chang Lee} have proved that the Dirichlet series associated with a modular form f of integral weight for the full modular group has an Euler product expansion if and only if f is an eigenfunction for finitely many explicitly given Hecke operators. In this paper the same problem has been considered for W. Kohnen's \(``+\) space'' of modular forms of half-integral weight for the congruence subgroup \(\Gamma _ 0(4)\). The methods used in this paper are completely different and simpler and also reduce very much the number of conditions given in the above paper for the modular forms over the full modular group.
Mathematics Subject Classification ID: 11F11
Mathematics Subject Classification ID: 11F67
Mathematics Subject Classification ID: 11F12
zbMATH DE Number: 4039993
zbMATH Keywords: Dirichlet series
zbMATH Keywords: Euler product expansion
zbMATH Keywords: Hecke operators
zbMATH Keywords: modular forms of half-integral weight
zbMATH Keywords: congruence subgroup
MaRDI profile type: Publication
cites work: Q4097001
cites work: Hecke operators on modular forms
cites work: Q3346401
cites work: Q4111656
cites work: On modular forms of half integral weight
full work available at URL: https://doi.org/10.1007/bf01194024
OpenAlex ID: W2007109305
description: scientific article; zbMATH DE number 4039993