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arXiv · 2101.01112

Congruences modulo powers of 5 for the rank parity function

Dandan Chen·Rong Chen·Frank Garvan
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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.

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Dandan Chen, Rong Chen, Frank Garvan. 2021-01-04. Congruences modulo powers of 5 for the rank parity function. https://arxiv.org/abs/2101.01112

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