10.46298/hrj.2021.7424
https://hrj.episciences.org/7424
Chen, Dandan
Dandan
Chen
Chen, Rong
Rong
Chen
Garvan, Frank
Frank
Garvan
Congruences modulo powers of 5 for the rank parity function
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.
episciences.org
Dyson's rank
partition congruences
mock theta functions
modular functions
2010 Mathematics Subject Classification. 05A17, 11F30, 11F37, 11P82, 11P83
[MATH]Mathematics [math]
2021-05-06
2021-05-06
2021-05-06
en
journal article
https://hal.archives-ouvertes.fr/hal-03208204v1
2804-7370
https://hrj.episciences.org/7424/pdf
VoR
application/pdf
Hardy-Ramanujan Journal
Volume 43 - Special Commemorative volume in honour of Srinivasa Ramanujan - 2020
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