arXiv subjects

Paul Beirne

Publications and source records attributed to Paul Beirne.

2 recordsLinked to original sources

arXiv2019

On the 2-head of the colored Jones polynomial for pretzel knots

In this paper, we prove a formula for the 2-head of the colored Jones polynomial for an infinite family of pretzel knots. Following Hall, the proof utilizes skein-theoretic techniques and a careful examination of higher order stability properties for coefficients of the colored Jones polynomial.

math.GT↗

arXiv2016

q-series and tails of colored Jones polynomials

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.

math.NT↗