q-series and tails of colored Jones polynomials

Abstract

We extend the table of Garoufalidis, Lê 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.

Twist regions and coefficients stability of the colored Jones polynomial

“…Moreover, infinite families of classical and new Ramanujan type q-series has been recently discovered and recovered using techniques that are related to the tail [2,8,[11][12][13]. The tail of the colored Jones polynomial has also been studied using classical q-series techniques [3,11,17]. Several connections between twist regions of a knot diagram and the colored Jones polynomial has been made.…”