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
Descripción
Sumario: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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