English

Incongruences for modular forms and applications to partition functions

Number Theory 2019-10-17 v1

Abstract

The study of arithmetic properties of coefficients of modular forms f(τ)=a(n)qnf(\tau) = \sum a(n)q^n has a rich history, including deep results regarding congruences in arithmetic progressions. Recently, work of C.-S. Radu, S. Ahlgren, B. Kim, N. Andersen, and S. L\"{o}brich have employed the qq-expansion principle of P. Deligne and M. Rapoport in order to determine more about where these congruences can occur. Here, we extend the method to give additional results for a large class of modular forms. We also give analogous results for generalized Frobenius partitions and the two mock theta functions f(q)f(q) and ω(q).\omega(q).

Keywords

Cite

@article{arxiv.1910.07051,
  title  = {Incongruences for modular forms and applications to partition functions},
  author = {Sharon Garthwaite and Marie Jameson},
  journal= {arXiv preprint arXiv:1910.07051},
  year   = {2019}
}

Comments

14 pages

R2 v1 2026-06-23T11:44:48.088Z