On Fourier coefficients of Maass wave forms of half integral weight belonging to Kohnen's spaces
type: Item
instance of: scholarly article
title: On Fourier coefficients of Maass wave forms of half integral weight belonging to Kohnen's spaces
zbMATH Open document ID: 0947.11021
author: Hisashi Kojima
published in: Tsukuba Journal of Mathematics
publication date: 2000-03-29T00:00:00Z
review text: Let \(f\) be an elliptic modular form of half-integral weight, which is a simultaneous Hecke eigenform. Let \(F\) correspond to \(f\) under the Shimura correspondence. \textit{J.-L. Waldspurger} [J. Math. Pure Appl. 60, 375-384 (1981; Zbl 0468.10014)] proved that the spares of the Fourier coefficients \(\alpha_f(n)\) at squarefree \(n\in \mathbb{N}\) are essentially proportional to the critical value of the zeta function attached to \(F\). The proportionality constant was derived later. In an earlier paper [J. Math. Soc. Japan 51, 615-730 (1999)] the author dealt with the analogous problem in some cases of modular forms \(f\) of half integral weight when the multiplicity is two. In the paper under review these results are generalized to the case of Maass wave forms of half integral weight belonging to Kohnen's space. The proof follows the same lines as in the earlier paper.
Mathematics Subject Classification ID: 11F37
Mathematics Subject Classification ID: 11F67
zbMATH DE Number: 1394756
zbMATH Keywords: Kohnen's space
zbMATH Keywords: Rankin convolution
zbMATH Keywords: theta series
zbMATH Keywords: Eisenstein series
zbMATH Keywords: elliptic modular form of half-integral weight
zbMATH Keywords: Maass wave forms
reviewed by: Aloys Krieg
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.21099/tkbjm/1496163876
OpenAlex ID: W1577079070
DOI: 10.21099/TKBJM/1496163876
description: scientific article; zbMATH DE number 1394756