Algebraic formulas for the coefficients of half-integral weight harmonic weak Maass forms
type: Item
instance of: scholarly article
title: Algebraic formulas for the coefficients of half-integral weight harmonic weak Maass forms
zbMATH Open document ID: 1304.11021
author: Jan Hendrik Bruinier
author: Ken Ono
published in: Advances in Mathematics
publication date: 2014-03-03T00:00:00Z
full work available at URL: https://arxiv.org/abs/1104.1182
review text: Let \(p(n)\) be the number of all partitions of natural number \(n\). It is well known the asymptotic formula for \(p(n)\) obtained by Hardy and Ramanujan expressing \(p(n)\) through certain exponential function and Rademacher's ``exact'' formula expressing \(p(n)\) as a Kloosterman sum and a modified Bessel function of the first kind. The authors obtains new formula for \(p(n)\), which expresses \(p(n)\) as a finite sum of singular moduli for a weak Maass form. The form is constructed using Dedekind's eta-function and quasimodular Eisenstein series. The sum of special values of the weak Maass form defines a ``trace'' \(T(n)\). In this paper, a formula it is obtained, where \(p(n)\) is expressed by this trace. Also it is provided an algorithm for computing \(p(n)\).
reviewed by: Guram Gogishvili
Mathematics Subject Classification ID: 11F11
Mathematics Subject Classification ID: 11P82
Mathematics Subject Classification ID: 11F27
zbMATH DE Number: 6264419
zbMATH Keywords: partition function
zbMATH Keywords: singular moduli
zbMATH Keywords: weak Maass form
zbMATH Keywords: Dedekind eta-function
zbMATH Keywords: Eisenstein series
MaRDI profile type: Publication
OpenAlex ID: W1990331738
arXiv ID: 1104.1182
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DOI: 10.1016/J.AIM.2013.05.028
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description: scientific article