Lehmer's conjecture for matrices over the ring of integers of some imaginary quadratic fields

الأصل · EN

Let R=O(√d) for d<0, squarefree, d≠ -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 λ₀=1.176....