Mock modular forms as $p$-adic modular forms

Kathrin Bringmann; Pavel Guerzhoy; Ben Kane

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arXiv · 1003.4465

Mock modular forms as $p$-adic modular forms

Kathrin Bringmann·Pavel Guerzhoy·Ben Kane

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Abstract

In this paper, we consider the question of correcting mock modular forms in order to obtain $p$-adic modular forms. In certain cases we show that a mock modular form $M^+$ is a $p$-adic modular form. Furthermore, we prove that otherwise the unique correction of $M^+$ is intimately related to the shadow of $M^+$.

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Kathrin Bringmann, Pavel Guerzhoy, Ben Kane. 2010-03-30. Mock modular forms as $p$-adic modular forms. https://arxiv.org/abs/1003.4465

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