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Congruences modulo powers of 5 for the rank parity function

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-03208204
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Submitted on : Monday, April 26, 2021 - 1:30:56 PM
Last modification on : Monday, March 28, 2022 - 8:14:08 AM
Long-term archiving on: : Tuesday, July 27, 2021 - 7:02:37 PM

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

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