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Mock modular forms as $p$-adic modular forms

2012; American Mathematical Society; Volume: 364; Issue: 5 Linguagem: Inglês

10.1090/s0002-9947-2012-05525-5

1088-6850

Kathrin Bringmann, Pavel Guerzhoy, Ben Kane,

Algebraic Geometry and Number Theory

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 $M^+$.