Mock modular forms as 𝑝-adic modular forms

Bringmann, Kathrin; Guerzhoy, Pavel; Kane, Ben

doi:10.1090/S0002-9947-2012-05525-5

Mock modular forms as $p$-adic modular forms
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by Kathrin Bringmann, Pavel Guerzhoy and Ben Kane PDF

Trans. Amer. Math. Soc. 364 (2012), 2393-2410 Request permission

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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