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Proceedings of the American Mathematical Society

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Vector-valued Maass-Poincaré series


Author: Sharon Anne Garthwaite
Journal: Proc. Amer. Math. Soc. 136 (2008), 427-436
MSC (2000): Primary 11F30; Secondary 11F37
DOI: https://doi.org/10.1090/S0002-9939-07-08961-7
Published electronically: November 1, 2007
MathSciNet review: 2358480
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Abstract: Shortly before his death, Ramanujan wrote about his discovery of mock theta functions, functions with interesting analytic properties. Recently, Zweger showed that mock theta functions could be “completed” to satisfy the transformation properties of a weight $1/2$ real analytic vector-valued modular form. Using Maass-Poincaré series, Bringmann and Ono proved the Andrews-Dragonette conjecture, establishing an exact formula for the coefficients of Ramanujan’s mock theta function $f(q)$. In this paper we study vector-valued Maass-Poincaré series of all weights, and give their Fourier expansions.


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Additional Information

Sharon Anne Garthwaite
Affiliation: Department of Mathematics, Bucknell University, Lewisburg, Pennsylvania 17837
Email: sharon.garthwaite@bucknell.edu

Received by editor(s): April 16, 2006
Received by editor(s) in revised form: October 17, 2006
Published electronically: November 1, 2007
Additional Notes: This research was supported by the University of Wisconsin at Madison NSF VIGRE program
Communicated by: Ken Ono
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.