We continue to investigate spt-type functions that arise from Bailey pairs. In this third paper on the subject, we proceed to introduce additional spt-type functions. We prove simple Ramanujan type congruences for these functions which can be explained by an spt-crank-type function. The spt-crank-type functions are actually defined first, with the spt-type functions coming from setting z = 1 in this definition. We find some of the spt-crank-type functions to have interesting representations as single series, some of which reduce to infinite products. Additionally, we find dissections of the other spt-crank-type functions when z is a certain root of unity. Both methods are used to explain congruences for the spt-type functions. Our series formulas require Bailey's Lemma and conjugate Bailey pairs. Our dissection formulas follow from Bailey's Lemma and dissections of known ranks and cranks.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa8193-2-2016,
author = {Chris Jennings-Shaffer},
title = {Exotic Bailey-Slater spt-functions III: Bailey pairs from groups B, F, G, and J},
journal = {Acta Arithmetica},
volume = {172},
year = {2016},
pages = {317-364},
zbl = {06602744},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa8193-2-2016}
}
Chris Jennings-Shaffer. Exotic Bailey-Slater spt-functions III: Bailey pairs from groups B, F, G, and J. Acta Arithmetica, Tome 172 (2016) pp. 317-364. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa8193-2-2016/