Just a brief note that my second paper on my thesis topic has been accepted by the Journal of Number Theory. The full citation is:

Graeme Taylor, Lehmer’s conjecture for matrices over the ring of integers of some imaginary quadratic fields, Journal of Number Theory, Volume 132, Issue 4, April 2012, Pages 590-607, ISSN 0022-314X, 10.1016/j.jnt.2011.09.006.
(http://www.sciencedirect.com/science/article/pii/S0022314X11002289)