Congruences modulo powers of 5 for the rank parity functionArticle
Authors: Dandan Chen 1,2; Rong Chen ; Frank Garvan
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Dandan Chen;Rong Chen;Frank Garvan
- 1 University of Shanghai [Shanghai]
- 2 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.
Volume: Volume 43 - Special Commemorative volume in honour of Srinivasa Ramanujan - 2020
Published on: May 6, 2021
Accepted on: May 6, 2021
Submitted on: April 30, 2021
Keywords: 2010 Mathematics Subject Classification. 05A17, 11F30, 11F37, 11P82, 11P83, [MATH]Mathematics [math], [en] modular functions, mock theta functions, Dyson's rank, partition congruences
Funding:
Source : OpenAIRE Graph- Adaptive Software Defined Terabit Transceiver for Flexible Optical Networks; Funder: European Commission; Code: 318714