$\ell$-adic properties of smallest parts functions

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 $\ell$-adic properties of certain modular forms and mock modular forms of weight $3/2$ with respect to the Hecke operators $T({\ell }^{2m})$.

References in corpus (2)

• Rank and crank moments for overpartitions
• Congruences for Andrews' spt-function modulo 32760 and extension of Atkin's Hecke-type partition congruences