Incongruences for modular forms and applications to partition functions
Abstract
The study of arithmetic properties of coefficients of modular forms f(τ) = Σ a(n)qn 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\"obrich have employed the q-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) and ω(q).
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