A geometric perspective on p adic properties of mock modular forms
AbstractBringmann et al. (Trans Am Math Soc 364(5):2393 2410, 2012) showed how to 'regularize' mock modular forms by a certain linear combination of the Eichler integral of their shadows in order to obtain p adic modular forms in the sense of Serre. In this paper, we give a new proof of a refined form of their results (for good primes p) by employing the geometric theory of harmonic Maass forms developed by Candelori (Math Ann 360(1 2):489 517, 2014) and the theory of overconvergent modular forms due to Katz and Coleman. In particular, our main results imply that the p adic modular forms in Bringmann et al. (2012) are overconvergent.