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Vector-Valued Maass-Poincaré Series
Sharon Anne Garthwaite
Proceedings of the American Mathematical Society
Vol. 136, No. 2 (Feb., 2008), pp. 427-436
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/20535107
Page Count: 10
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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.
Proceedings of the American Mathematical Society © 2008 American Mathematical Society