Rogers-Ramanujan type identities for alternating knots

TL;DR

This paper uses q-series techniques to prove Rogers-Ramanujan type identities related to alternating knots, confirming conjectures by Garoufalidis, Le, and Zagier.

Contribution

It introduces new Rogers-Ramanujan type identities for alternating knots and proves them using q-series methods, advancing the connection between knot theory and q-series.

Findings

Proved Rogers-Ramanujan type identities for alternating knots.

Confirmed conjectures by Garoufalidis, Le, and Zagier.

Demonstrated the effectiveness of q-series techniques in knot theory.

Abstract

We highlight the role of q-series techniques in proving identities arising from knot theory. In particular, we prove Rogers-Ramanujan type identities for alternating knots as conjectured by Garoufalidis, Le and Zagier.