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arXiv · 1602.01036

A note on cusp forms as $p$-adic limits

Scott Ahlgren·Detchat Samart
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Abstract

Several authors have recently proved results which express cusp forms as $p$-adic limits of weakly holomorphic modular forms under repeated application of Atkin's $U$-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 $p$-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.

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Scott Ahlgren, Detchat Samart. 2016-02-02. A note on cusp forms as $p$-adic limits. https://arxiv.org/abs/1602.01036

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