Exotic Bailey-Slater spt-functions III: Bailey pairs from groups B, F, G, and J

• Autorzy: Chris Jennings-Shaffer
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11P83: Partitions; congruences and congruential restrictions
• 11P81: Elementary theory of partitions
• 33D15: Basic hypergeometric functions in one variable, r φ s

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2016
• Tom: 173
• Numer: 4
• Strony: 317-364

Daty

wydano

2016

Twórcy

autor

Chris Jennings-Shaffer

• Department of Mathematics, Oregon State University, Kidder Hall 368, Corvallis, OR 97331, U.S.A.

Identyfikatory

DOI

10.4064/aa8193-2-2016