Remarks on Kohnen-Zagier's paper concerning Fourier coefficients of modular forms of half integral weight
type: Item
instance of: scholarly article
title: Remarks on Kohnen-Zagier's paper concerning Fourier coefficients of modular forms of half integral weight
zbMATH Open document ID: 0808.11032
author: Hisashi Kojima
published in: Proceedings of the Japan Academy. Series A
publication date: 1994-08-08T00:00:00Z
review text: Let \(\psi\) denote Shimura's correspondence between elliptic modular forms of half-integral and even weight. Consider a Hecke eigenform \(f\) in Kohnen's ``+''-space \(S^ +_{k+ 1/2}(4)\) with Fourier coefficients \(a(n)\), \(n\geq 1\). \textit{W. Kohnen} and \textit{D. Zagier} [Invent. Math. 64, 175-198 (1981; Zbl 0468.10015)] explicitly determined the proportionality of \(a(n)^ 2\) for square free \(n\) with a special value of the zeta function associated with \(\psi(f)\). In the paper under review the author announces the analogous result for a Hecke eigenform \(f\in S_{k+1/2} (4N)\) resp. \(f\in S_{k+1/2} (4N,\chi_ N)\) such that \(\psi(f)\) is a primitive form in \(S_{2k} (2N)\).
Mathematics Subject Classification ID: 11F37
Mathematics Subject Classification ID: 11F11
Mathematics Subject Classification ID: 11F67
zbMATH DE Number: 597326
zbMATH Keywords: half-integral weight
zbMATH Keywords: Shimura correspondence
zbMATH Keywords: Hecke operators
zbMATH Keywords: special value of zeta function
zbMATH Keywords: elliptic modular forms
zbMATH Keywords: Fourier coefficients
zbMATH Keywords: Hecke eigenform
reviewed by: Aloys Krieg
MaRDI profile type: Publication
full work available at URL: pjaa.69.383
OpenAlex ID: W1977478355
cites work: Values of L-series of modular forms at the center of the critical strip
cites work: Fourier coefficients and modular forms of half-integral weight
cites work: Modular forms of half integral weight and the integral of certain theta-functions
cites work: On Shimura’s trace formula
cites work: On modular forms of half integral weight
cites work: The critical values of certain zeta functions associated with modular forms of half-integral weight
cites work: The decomposition of the spaces of cusp forms of half-integral weight and trace formula of Hecke operators
cites work: Shimura and Shintani correspondences
cites work: Sur les coefficients de Fourier des formes modulaires de poids demi-entier
DOI: 10.3792/PJAA.69.383
description: scientific article; zbMATH DE number 597326