Vector-valued Maass-Poincaré series

Garthwaite, Sharon

doi:10.1090/S0002-9939-07-08961-7

Vector-valued Maass-Poincaré series
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by Sharon Anne Garthwaite PDF

Proc. Amer. Math. Soc. 136 (2008), 427-436 Request permission

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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