[Abstract] F.G. Garvan and C. Jennings-Shaffer; Exotic Bailey-Slater SPT-functions II: Hecke-Rogers-type double sums and Bailey pairs From groups A, C, E , Adv. Math. 299 (2016), 605-639.


Abstract:

We continue to investigate spt-type functions that arise from Bailey pairs. We prove simple Ramanujan type congruences for these functions which can be explained by a spt-crank-type function. The spt-crank-type functions are constructed by adding an extra variable into the generating functions. We find these generating functions to have interesting representations as either infinite products or as Hecke-Rogers-type double series. These series reduce nicely when is a certain root of unity and allow us to deduce congruences. Additionally we find dissections when is a certain root of unity to explain the congruences. Our double sum and product formulas require Bailey's Lemma and conjugate Bailey pairs. Our dissection formulas follow from Bailey's Lemma and dissections of known ranks and cranks.

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Created by F.G. Garvan (fgarvan@ufl.edu) on Wednesday, Janury 28, 2015.
Last update made Thu Aug 4 14:59:43 EDT 2016.

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