A note on cusp forms as $p$-adic limits
Number Theory
2016-02-03 v1
Abstract
Several authors have recently proved results which express cusp forms as -adic limits of weakly holomorphic modular forms under repeated application of Atkin's -operator. The proofs involve techniques from the theory of weak harmonic Maass forms, and in particular a result of Guerzhoy, Kent, and Ono on the -adic coupling of mock modular forms and their shadows. Here we obtain strengthened versions of these results using techniques from the theory of holomorphic modular forms.
Cite
@article{arxiv.1602.01036,
title = {A note on cusp forms as $p$-adic limits},
author = {Scott Ahlgren and Detchat Samart},
journal= {arXiv preprint arXiv:1602.01036},
year = {2016}
}