The Bailey chain and mock theta functions

Abstract

Standard applications of the Bailey chain preserve mixed mock modularity but not mock modularity. After illustrating this with some examples, we show how to use a change of base in Bailey pairs due to Bressoud, Ismail and Stanton to explicitly construct families of q-hypergeometric multisums which are mock theta functions. We also prove identities involving some of these multisums and certain classical mock theta functions.

17 pages, to appear in Advances in Mathematics

References in corpus (6)

• Mock Theta Functions
• Quantum Black Holes, Wall Crossing, and Mock Modular Forms
• Hecke-type double sums, Appell-Lerch sums, and mock theta functions (I)
• Lectures on Quantum Black Holes
• Rogers-Ramanujan type identities and the head and tail of the colored Jones polynomial
• On three third order mock theta functions and Hecke-type double sums

Cited by in corpus (8)

• Dyson's Ranks and Appell-Lerch Sums
• A $q$-series identity via the ${\mathfrak{sl}}_3$ colored Jones polynomials for the $(2,2m)$-torus link
• Eulerian series as modular forms revisited
• An Efficient Algorithm to Compute the Colored Jones Polynomial
• More on some Mock theta Double sums
• Mixed mock modular q-series
• The tail of a quantum spin network
• A general double sum identity, mock theta functions, and Bailey pairs