Congruences for a mock modular form on SL2(Z) and the smallest parts function

Scott Ahlgren, Byungchan Kim

Research output: Contribution to journalArticle


Using a family of mock modular forms constructed by Zagier, we study the coefficients of a mock modular form of weight 3/2 on SL2(Z) modulo primes ℓ≥5. These coefficients are related to the smallest parts function of Andrews. As an application, we reprove a theorem of Garvan regarding the properties of this function modulo ℓ. As another application, we show that congruences modulo ℓ for the smallest parts function are rare in a precise sense.

Original languageEnglish (US)
Pages (from-to)81-89
Number of pages9
JournalJournal of Number Theory
StatePublished - Aug 2018


  • Mock modular forms
  • Modular forms modulo ℓ
  • Smallest parts function

ASJC Scopus subject areas

  • Algebra and Number Theory

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