location:  Publications → journals → CJM
Abstract view

# Non-Existence of Ramanujan Congruences in Modular Forms of Level Four

Published:2011-04-30
Printed: Dec 2011
• Michael Dewar,
Department of Mathematics and Statistics, Queen's University, Kingston, ON
 Format: HTML LaTeX MathJax PDF

## Abstract

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

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