Mahler measure of the colored Jones polynomial and the volume conjecture
arXiv:math/0206249
Abstract
In this note, I will discuss a possible relation between the Mahler measure of the colored Jones polynomial and the volume conjecture. In particular, I will study the colored Jones polynomial of the figure-eight knot on the unit circle. I will also propose a method to prove the volume conjecture for satellites of the figure-eight knot.
arXiv comment14 pages, 11 figures, submitted to the proceedings of the workshop `Volume Conjecture and Its Related Topics' held at the International Institute for Advanced Studies from 5th to 8th March, 2002
References in corpus (4)
- On the volume conjecture for hyperbolic knots
- Optimistic calculations about the Witten--Reshetikhin--Turaev invariants of closed three-manifolds obtained from the figure-eight knot by integral Dehn surgeries
- The asymptotic behavior of the colored Jones function of a knot and its volume
- Mahler measure, links and homology growth