Hardy Ramanujan Journal |

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.

Source : oai:HAL:hal-03208204v1

Volume: Volume 43 - Special Commemorative volume in honour of Srinivasa Ramanujan

Published 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]

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