{"docId":7424,"paperId":7424,"url":"https:\/\/hrj.episciences.org\/7424","doi":"10.46298\/hrj.2021.7424","journalName":"Hardy-Ramanujan Journal","issn":"","eissn":"2804-7370","volume":[{"vid":438,"name":"Volume 43 - Special Commemorative volume in honour of Srinivasa Ramanujan - 2020"}],"section":[],"repositoryName":"Hal","repositoryIdentifier":"hal-03208204","repositoryVersion":1,"repositoryLink":"https:\/\/hal.archives-ouvertes.fr\/hal-03208204v1","dateSubmitted":"2021-04-30 14:17:53","dateAccepted":"2021-05-06 14:52:05","datePublished":"2021-05-06 14:52:27","titles":{"en":"Congruences modulo powers of 5 for the rank parity function"},"authors":["Chen, Dandan","Chen, Rong","Garvan, Frank"],"abstracts":{"en":"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."},"keywords":[{"en":"Dyson's rank"},{"en":"partition congruences"},{"en":"mock theta functions"},{"en":"modular functions"},"2010 Mathematics Subject Classification. 05A17, 11F30, 11F37, 11P82, 11P83","[MATH]Mathematics [math]"]}