## Dandan Chen ; Rong Chen ; Frank Garvan - Congruences modulo powers of 5 for the rank parity function

hrj:7424 - Hardy-Ramanujan Journal, May 6, 2021, Volume 43 - Special Commemorative volume in honour of Srinivasa Ramanujan - 2020 - https://doi.org/10.46298/hrj.2021.7424
Congruences modulo powers of 5 for the rank parity function

Authors: Dandan Chen ; Rong Chen ; Frank Garvan

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 modulo powers of 5 for the rank parity function.

Volume: Volume 43 - Special Commemorative volume in honour of Srinivasa Ramanujan - 2020
Published on: May 6, 2021
Accepted on: May 6, 2021
Submitted on: April 30, 2021
Keywords: Dyson's rank,partition congruences,mock theta functions,modular functions,2010 Mathematics Subject Classification. 05A17, 11F30, 11F37, 11P82, 11P83,[MATH]Mathematics [math]