# Mock modular forms as $p$-adic modular forms

@article{Bringmann2010MockMF,
title={Mock modular forms as \$p\$-adic modular forms},
author={Kathrin Bringmann and P. Guerzhoy and Ben Kane},
journal={Transactions of the American Mathematical Society},
year={2010},
volume={364},
pages={2393-2410}
}
• Published 23 March 2010
• Mathematics
• Transactions of the American Mathematical Society
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.
On $p$-adic harmonic Maass functions
Modular and mock modular forms possess many striking p-adic properties, as studied by Bringmann, Guerzhoy, Kane, Kent, Ono, and others. Candelori developed a geometric theory of harmonic Maass forms
Modular and mock modular forms possess many striking $p$-adic properties, as studied by Bringmann, Guerzhoy, Kane, Kent, Ono, and others. Candelori developed a geometric theory of harmonic Maass