Lehmer's conjecture for matrices over the ring of integers of some   imaginary quadratic fields
  Let $R=\mathcal{O}_{\Q(\sqrt{d})}$ for $d<0$, squarefree, $d\neq -1,-3$. We prove Lehmer's conjecture for associated reciprocal polynomials of $R$-matrices; that is, any noncyclotomic $R$-matrix has Mahler measure at least $\lambda_0=1.176...$. 
G. Taylor
math.NT