Fourier coefficients of modular forms of half integral weight, periods of modular forms and the special values of zeta functions
type: Item
instance of: scholarly article
title: Fourier coefficients of modular forms of half integral weight, periods of modular forms and the special values of zeta functions
zbMATH Open document ID: 0893.11017
author: Hisashi Kojima
published in: Hiroshima Mathematical Journal
publication date: 1998-08-24T00:00:00Z
review text: The author investigates relations between Fourier coefficients of modular forms of half integral weight and special values of zeta functions associated with the corresponding modular forms \(F\) of integral weight. To that end, periods of modular forms are first expressed as finite sums of special values of modified zeta functions associated with modular forms. The values of these modified zeta functions are further expressed in terms of special values of the zeta functions \(L(s,F,\psi) =\sum^\infty_{n=1} A(n)\psi (n)n^{-s}\) with Dirichlet characters \(\psi\). This leads to the result that the Fourier coefficients of the Shintani lift of \(F\) can be explicitly expressed in terms of special values of the zeta functions \(L(s,F, \psi)\). The author's results also yield a result on the arithmeticity of the fundamental periods of modular forms. The author's results moreover give an expression for the Fourier coefficients of Jacobi forms in terms of special values of zeta functions associated with modular forms of integral weight.
Mathematics Subject Classification ID: 11F37
Mathematics Subject Classification ID: 11F30
Mathematics Subject Classification ID: 11F67
Mathematics Subject Classification ID: 11F11
zbMATH DE Number: 1079838
zbMATH Keywords: Fourier coefficients of modular forms of half integral weight
zbMATH Keywords: special values of zeta functions
zbMATH Keywords: Shintani lift
zbMATH Keywords: fundamental periods of modular forms
zbMATH Keywords: Fourier coefficients of Jacobi forms
reviewed by: Jürgen Elstrodt
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.32917/hmj/1206127051
OpenAlex ID: W1561486317
Wikidata QID: Q128870718
DOI: 10.32917/HMJ/1206127051
description: scientific article; zbMATH DE number 1079838