English

Congruences for modular forms and generalized Frobenius partitions

Number Theory 2018-09-05 v1

Abstract

The partition function is known to exhibit beautiful congruences that are often proved using the theory of modular forms. In this paper, we study the extent to which these congruence results apply to the generalized Frobenius partitions defined by Andrews. In particular, we prove that there are infinitely many congruences for cϕk(n)c\phi_k(n) modulo ,\ell, where gcd(,6k)=1,\gcd(\ell,6k)=1, and we also prove results on the parity of cϕk(n).c\phi_k(n). Along the way, we prove results regarding the parity of coefficients of weakly holomorphic modular forms which generalize work of Ono.

Keywords

Cite

@article{arxiv.1809.00666,
  title  = {Congruences for modular forms and generalized Frobenius partitions},
  author = {Marie Jameson and Maggie Wieczorek},
  journal= {arXiv preprint arXiv:1809.00666},
  year   = {2018}
}

Comments

This is a pre-print. Comments are appreciated

R2 v1 2026-06-23T03:52:58.098Z