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 | References | Similar Articles | Additional Information

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 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 . 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

DOI:
http://dx.doi.org/10.1090/S0002-9939-07-08961-7

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.