q-series and tails of colored Jones polynomials

TL;DR

This paper extends and proves new Rogers-Ramanujan type identities for the tails of colored Jones polynomials of alternating knots up to 10 crossings using q-series methods.

Contribution

It generalizes existing conjectures to a broader class of knots and provides rigorous proofs for these identities.

Findings

New identities for tails of colored Jones polynomials

Verification of conjectural identities for knots up to 10 crossings

Application of q-series techniques to knot invariants

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.