A note on cusp forms as p-adic limits

Scott Ahlgren, Detchat Samart

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)360-373
Number of pages14
JournalJournal of Number Theory
Volume168
DOIs
StatePublished - Nov 1 2016

Keywords

  • Cusp forms as p-adic limits
  • Modular forms

ASJC Scopus subject areas

  • Algebra and Number Theory

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