Effective congruences for mock theta functions
type: Item
instance of: scholarly article
title: Effective congruences for mock theta functions
zbMATH Open document ID: 1302.11083
author: Nickolas Andersen
author: Holley Friedlander
author: Jeremy Fuller
author: Heidi Goodson
published in: Mathematics
publication date: 2014-08-27T00:00:00Z
full work available at URL: https://arxiv.org/abs/1304.3136
review text: Summary: Let \(M(q)=\sum c(n)q^n\) be one of Ramanujan's mock theta functions. We establish the existence of infinitely many linear congruences of the form: \[ c(An+B)\equiv 0\pmod{\ell^j} \] where A is a multiple of \(\ell\) and an auxiliary prime, \(p\). Moreover, we give an effectively computable upper bound on the smallest such \(p\) for which these congruences hold. The effective nature of our results is based on the prior works of \textit{S. Lichtenstein} [Proc. Am. Math. Soc. 136, No. 10, 3419--3428 (2008; Zbl 1247.11069)] and \textit{S. Treneer} [ibid. (3) 93, No. 2, 304--324 (2006; Zbl 1165.11316)].
Mathematics Subject Classification ID: 11P83
Mathematics Subject Classification ID: 11F37
zbMATH DE Number: 6334779
zbMATH Keywords: mock theta functions
zbMATH Keywords: congruences
zbMATH Keywords: harmonic weak Maass forms
MaRDI profile type: Publication
OpenAlex ID: W1967818586
arXiv ID: 1304.3136
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DOI: 10.3390/MATH1030100
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description: scientific article; zbMATH DE number 6334779