Work

Universal mock theta functions and two-variable Hecke-Rogers identities

Year: 2014

Type: preprint

Abstract: We obtain two-variable Hecke-Rogers identities for three universal mock theta functions. This implies that many of Ramanujan's mock theta functions, including all the third order functions, have a Hecke-Rogers-type double sum representation. We find new generating function identities for the Dyson rank function, the overpartition rank function, the M2-rank function and related spt-crank functions. Results are proved using the theory of basic hypergeometric functions.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1402.1884

Author: Garvan, Frank

Institutions: Rutgers, The State University of New Jersey, University of Florida

Language: English

Topic: Advanced Mathematical Identities

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2950868689

Cites: 25

Cited by: 2

Related to: 20