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

Abstract

Let $R=\mathcal{O}_{\Q(\sqrt{d})}$ for $d<0$, squarefree, $d\ne -1,-3$. We prove Lehmer's conjecture for associated reciprocal polynomials of $R$-matrices; that is, any noncyclotomic $R$-matrix has Mahler measure at least ${\lambda }_0=\mathrm{1.176...}$.

References in corpus (1)

• Integer symmetric matrices of small spectral radius and small Mahler measure