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 language | English (US) |
|---|---|
| Pages (from-to) | 629-645 |
| Number of pages | 17 |
| Journal | Advances in Mathematics |
| Volume | 228 |
| Issue number | 1 |
| DOIs | |
| State | Published - 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
- General Mathematics