Congruences modulo powers of 5 for the rank parity function
Number Theory
2021-01-05 v1 Combinatorics
Abstract
It is well known that Ramanujan conjectured congruences modulo powers of 5, 7 and and 11 for the partition function. These were subsequently proved by Watson (1938) and Atkin (1967). In 2009 Choi, Kang, and Lovejoy proved congruences modulo powers of 5 for the crank parity function. The generating function for rank parity function is f(q), which is the first example of a mock theta function that Ramanujan mentioned in his last letter to Hardy. We prove congruences modulo powers of 5 for the rank parity function.
Cite
@article{arxiv.2101.01112,
title = {Congruences modulo powers of 5 for the rank parity function},
author = {Dandan Chen and Rong Chen and Frank Garvan},
journal= {arXiv preprint arXiv:2101.01112},
year = {2021}
}
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25 pages