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

Nickolas Andersen; Kathrin Bringmann; Larry Rolen

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arXiv · 1612.00051

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

Nickolas Andersen·Kathrin Bringmann·Larry Rolen

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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 Poincaré 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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Nickolas Andersen, Kathrin Bringmann, Larry Rolen. 2016-11-30. Images of Maass-Poincaré series in the lower half-plane. https://arxiv.org/abs/1612.00051

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