Holomorphic projections and Ramanujan's mock theta functions

We use 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 th...

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Bibliographic Details
Published in:Proceedings of the National Academy of Sciences - PNAS 2014-03, Vol.111 (11), p.3961-3967
Main Authors: Imamoğlu, Özlem, Raum, Martin, Richter, Olav K.
Format: Article
Language:English
Subjects:
Coefficients
Combinatorics
Constant coefficients
Fourier Analysis
Fourier coefficients
Fourier series
Mathematical functions
Mathematical theorems
Mathematics
Models, Theoretical
Number theory
Physical Sciences
Projection of vectors
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Summary:We use 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:0027-8424
1091-6490
DOI:10.1073/pnas.1311621111