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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
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

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.