A geometric perspective on p-adic properties of mock modular forms

Luca Candelori, Francesc Castella

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

Bringmann 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.

Original languageEnglish (US)
Article number5
JournalResearch in Mathematical Sciences
Volume4
Issue number1
DOIs
StatePublished - Dec 1 2017

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Mathematics (miscellaneous)
  • Computational Mathematics
  • Applied Mathematics

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