Images of Maass-Poincaré series in the lower half-plane

Published 30 Nov 2016 in math.NT | (1612.00051v1)

Abstract: In this note we extend integral weight harmonic Maass forms to functions defined on the upper and lower half-planes using the method of Poincar\'e series. This relates to Rademacher's "expansion of zero" principle, which was recently employed by Rhoades to link mock theta functions and partial theta functions.

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