Integral traces of singular values of weak Maass forms
type: Item
instance of: scholarly article
title: Integral traces of singular values of weak Maass forms
zbMATH Open document ID: 1215.11046
author: J. Martínez
published in: Algebra \& Number Theory
publication date: 2009-03-16T00:00:00Z
review text: For a holomorphic modular form, one can define traces of the form which are essentially the toric periods studied by \textit{J.-L. Waldspurger} [Compos. Math. 54, 173--242 (1985; Zbl 0567.10021)]. Waldspurger showed the square of the traces are the central values of base change \(L-\)functions. This together with his result on Shimura correspondence, implies the square of the traces are (up to a scalar multiple) the squares of Fourier coefficients of a holomorphic half integral weight form. \textit{W. Kohnen} [Math. Ann. 271, 237--268 (1985; Zbl 0542.10018)] proved that the traces are indeed (up to a scalar multiple) the Fourier coefficients of a holomorphic half integral weight form. The paper proved a corresponding result in the case of weakly holomorphic modular form. For a level 1 weakly holomorphic modular form, the authors used its traces as Fourier coefficients to construct a half integral weight weakly holomorphic form. This gives a Zagier lift, the negative weight analogue of Shintani lift. Moreover they showed that if the original integral weight form has integer coefficients, so does its Zagier lift.
reviewed by: Zhengyu Mao
Mathematics Subject Classification ID: 11F30
Mathematics Subject Classification ID: 11F37
zbMATH DE Number: 5529338
zbMATH Keywords: weak Maass forms
zbMATH Keywords: weakly holomorphic modular forms
zbMATH Keywords: traces of singular moduli
MaRDI profile type: Publication
full work available at URL: ant.2008.2.573
OpenAlex ID: W1971411600
DOI: 10.2140/ANT.2008.2.573
description: scientific article; zbMATH DE number 5529338