Holomorphic projections and Ramanujan's mock theta functions

We employ spectral methods of automorphic forms to establish a holomorphic projection operator for tensor products of vector-valued harmonic weak Maass forms and vector-valued modular forms. We apply this operator to discover simple recursions for Fourier series coefficients of Ramanujan's mock...

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Bibliographic Details
Published in:arXiv.org 2014-02
Main Authors: Imamoglu, Özlem, Raum, Martin, Richter, Olav K
Format: Article
Language:English
Subjects:
Fourier series
Mathematical analysis
Spectral methods
Tensors
Online Access:Get full text
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Summary:We employ spectral methods of automorphic forms to establish a holomorphic projection operator for tensor products of vector-valued harmonic weak Maass forms and vector-valued modular forms. We apply this operator to discover simple recursions for Fourier series coefficients of Ramanujan's mock theta functions.
ISSN:2331-8422
DOI:10.48550/arxiv.1306.3919