Completions and algebraic formulas for the coefficients of Ramanujan’s mock theta functions

We present completions of mock theta functions to harmonic weak Maass forms of weight [Formula: see text] and algebraic formulas for the coefficients of mock theta functions. We give several harmonic weak Maass forms of weight [Formula: see text] that have mock theta functions as their holomorphic p...

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Detalles Bibliográficos
Autores principales: Klein, David, Kupka, Jennifer
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer US 2020
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8599414/
https://www.ncbi.nlm.nih.gov/pubmed/34840518
http://dx.doi.org/10.1007/s11139-020-00324-4
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author Klein, David
Kupka, Jennifer
author_facet Klein, David
Kupka, Jennifer
author_sort Klein, David
collection PubMed
description We present completions of mock theta functions to harmonic weak Maass forms of weight [Formula: see text] and algebraic formulas for the coefficients of mock theta functions. We give several harmonic weak Maass forms of weight [Formula: see text] that have mock theta functions as their holomorphic part. Using these harmonic weak Maass forms and the Millson theta lift, we compute finite algebraic formulas for the coefficients of the appearing mock theta functions in terms of traces of singular moduli.
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spelling pubmed-85994142021-11-24 Completions and algebraic formulas for the coefficients of Ramanujan’s mock theta functions Klein, David Kupka, Jennifer Ramanujan J Article We present completions of mock theta functions to harmonic weak Maass forms of weight [Formula: see text] and algebraic formulas for the coefficients of mock theta functions. We give several harmonic weak Maass forms of weight [Formula: see text] that have mock theta functions as their holomorphic part. Using these harmonic weak Maass forms and the Millson theta lift, we compute finite algebraic formulas for the coefficients of the appearing mock theta functions in terms of traces of singular moduli. Springer US 2020-10-20 2021 /pmc/articles/PMC8599414/ /pubmed/34840518 http://dx.doi.org/10.1007/s11139-020-00324-4 Text en © The Author(s) 2020 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Klein, David
Kupka, Jennifer
Completions and algebraic formulas for the coefficients of Ramanujan’s mock theta functions
title Completions and algebraic formulas for the coefficients of Ramanujan’s mock theta functions
title_full Completions and algebraic formulas for the coefficients of Ramanujan’s mock theta functions
title_fullStr Completions and algebraic formulas for the coefficients of Ramanujan’s mock theta functions
title_full_unstemmed Completions and algebraic formulas for the coefficients of Ramanujan’s mock theta functions
title_short Completions and algebraic formulas for the coefficients of Ramanujan’s mock theta functions
title_sort completions and algebraic formulas for the coefficients of ramanujan’s mock theta functions
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8599414/
https://www.ncbi.nlm.nih.gov/pubmed/34840518
http://dx.doi.org/10.1007/s11139-020-00324-4
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