Lehmer's conjecture for Hermitian matrices over the Eisenstein and   Gaussian integers
  We solve Lehmer's problem for a class of polynomials arising from Hermitian matrices over the Eisenstein and Gaussian integers, that is, we show that all such polynomials have Mahler measure at least Lehmer's number \tau_0 = 1.17628... . 
Gary Greaves and Graeme Taylor
math.NT