English

$\ell$-adic properties of smallest parts functions

Number Theory 2013-06-10 v1

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 3/23/2 with respect to the Hecke operators T(2m)T(\ell^{2m}).

Keywords

Cite

@article{arxiv.1011.6079,
  title  = {$\ell$-adic properties of smallest parts functions},
  author = {Scott Ahlgren and Kathrin Bringmann and Jeremy Lovejoy},
  journal= {arXiv preprint arXiv:1011.6079},
  year   = {2013}
}