Congruences modulo powers of 5 for the rank parity function

Dandan Chen (1) , Rong Chen , Frank Garvan

1 Shanghai University

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.

Mots clés: modular functions; mock theta functions; Dyson's rank; partition congruences

Domaines: Mathématiques [math]

Dandan Chen, Rong Chen, Frank Garvan. Congruences modulo powers of 5 for the rank parity function. Hardy-Ramanujan Journal, 2021, Volume 43 - Special Commemorative volume in honour of Srinivasa Ramanujan - 2020, pp.24-45. ⟨10.46298/hrj.2021.7424⟩. ⟨hal-03208204⟩