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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
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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Kathrin Bringmann and Ken Ono, Arithmetic properties of coefficients of half-integral weight Maass-Poincaré series, Mathematische Annalen, 337 (2007). 591-612.
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 . Vol. 2, Lecture Notes in Mathematics, vol. 1001, Springer-Verlag, Berlin, 1983. MR 711197 (86e:11040)
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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
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
Article copyright:
© Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
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