Mahler measure of the colored Jones polynomial and the volume conjecture

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.

14 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