ℓ-adic properties of smallest parts functions

Scott Ahlgren, Kathrin Bringmann, Jeremy Lovejoy

Research output: Contribution to journalArticlepeer-review

Abstract

We prove explicit congruences modulo powers of arbitrary primes for three smallest parts functions: one for partitions, one for overpartitions, and one for partitions without repeated odd parts. The proofs depend on ℓ-adic properties of certain modular forms and mock modular forms of weight 3/2 with respect to the Hecke operators T(ℓ2m).

Original languageEnglish (US)
Pages (from-to)629-645
Number of pages17
JournalAdvances in Mathematics
Volume228
Issue number1
DOIs
StatePublished - Sep 10 2011

Keywords

  • 11F37
  • 11P83
  • Congruences
  • Harmonic weak Maass forms
  • Hecke operators
  • Mock modular forms
  • Overpartitions
  • Partitions
  • Smallest parts functions

ASJC Scopus subject areas

  • Mathematics(all)

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