Non-existence of Ramanujan congruences in modular forms of level four
Number Theory
2019-08-15 v1
Abstract
Ramanujan famously found congruences for the partition function like p(5n+4) = 0 modulo 5. 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) which 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
Cite
@article{arxiv.0910.0065,
title = {Non-existence of Ramanujan congruences in modular forms of level four},
author = {Michael Dewar},
journal= {arXiv preprint arXiv:0910.0065},
year = {2019}
}
Comments
19 pages