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ISSN 1088-6826(e) ISSN 0002-9939(p)

Vector-valued Maass-Poincaré series

Author(s): Sharon Anne Garthwaite
Journal: Proc. Amer. Math. Soc. 136 (2008), 427-436.
MSC (2000): Primary 11F30; Secondary 11F37
Posted: 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 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: 10.1090/S0002-9939-07-08961-7
PII: S 0002-9939(07)08961-7
Received by editor(s): April 16, 2006
Received by editor(s) in revised form: October 17, 2006
Posted: November 1, 2007
Additional Notes: This research was supported by the University of Wisconsin at Madison NSF VIGRE program
Communicated by: Ken Ono
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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