q-series and tails of colored Jones polynomials

Abstract

We extend the table of Garoufalidis, Le and Zagier concerning conjectural Rogers-Ramanujan type identities for tails of colored Jones polynomials to all alternating knots up to 10 crossings. We then prove these new identities using q-series techniques.

15 pages, to appear in Indagationes Mathematicae

References in corpus (1)

• Sequencing BPS Spectra

Cited by in corpus (2)

• Coloured ${\mathfrak{sl}}_r$ invariants of torus knots and characters of ${\mathcal{W}}_r$ algebras
• The zero stability for the one-row colored ${\mathfrak{sl}}_3$ Jones polynomial