Ramanujan famously found congruences like $p(5n+4)\equiv 0 \operatorname{mod} 5$ for the partition function. We provide a method to find all simple congruences of this type in the coefficients of the inverse of a modular form on $\Gamma_{1}(4)$ that is non-vanishing on the upper half plane. This is applied to answer open questions about the (non)-existence of congruences in the generating functions for overpartitions, crank differences, and 2-colored $F$-partitions.

Keywords:

modular form, Ramanujan congruence, generalized Frobenius partition, overpartition, crank modular form, Ramanujan congruence, generalized Frobenius partition, overpartition, crank

MSC Classifications:

11F33, 11P83 show english descriptions Congruences for modular and $p$-adic modular forms [See also 14G20, 22E50]
Partitions; congruences and congruential restrictions 11F33 - Congruences for modular and $p$-adic modular forms [See also 14G20, 22E50]
11P83 - Partitions; congruences and congruential restrictions

top of page | contact us | social media | privacy | site map