# Congruences modulo powers of 5 for the rank parity function

```@article{Chen2021CongruencesMP,
title={Congruences modulo powers of 5 for the rank parity function},
author={Dandan Chen and Rong Chen and Frank G. Garvan},
journal={Hardy-Ramanujan Journal},
year={2021}
}```
• Published 4 January 2021
• Mathematics
• Hardy-Ramanujan Journal
International audience It is well known that Ramanujan conjectured congruences modulo powers of 5, 7 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 the 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…
2 Citations

### Generating Functions of the Hurwitz Class Numbers Associated with Certain Mock Theta Functions

• Mathematics
• 2021
We find Hecke-Rogers type series representations of generating functions of the Hurwitz class numbers which are similar to certain mock theta functions. We also prove two combinatorial

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