On ranks and cranks of partitions modulo 4 and 8

@article{Mortenson2019OnRA,
  title={On ranks and cranks of partitions modulo 4 and 8},
  author={Eric T. Mortenson},
  journal={J. Comb. Theory, Ser. A},
  year={2019},
  volume={161},
  pages={51-80}
}
A mock theta function identity related to the partition rank modulo 3 and 9
TLDR
A new mock theta function identity related to the partition rank modulo 3 and 9 is proved and the dissection of the rank generating function modulo [Formula: see text] is obtained.
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In this paper we prove some identities, conjectured by Lewis, for the rank and crank of partitions concerning the modulo 4 and 8. These identities are similar to Dyson's identities for the rank
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In 2005, using a famous lemma of Atkin and Swinnerton-Dyer (Some properties of partitions, Proc. Lond. Math. Soc. (3) 4 (1954), 84–106), Yesilyurt (Four identities related to third order mock theta
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In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge, to examine the papers of the late G.N. Watson. Among these papers, Andrews
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By introducing a dual notion between partial theta functions and Appell–Lerch sums, we find and prove a formula which expresses Hecke‐type double sums in terms of Appell–Lerch sums. Not only does our
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