Lehmer's conjecture for Hermitian matrices over the Eisenstein and Gaussian integers

Abstract

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 τ_0 = 1.17628... .

References in corpus (2)

• A very short proof of Cauchy's interlace theorem for eigenvalues of Hermitian matrices
• Cyclotomic matrices over the Eisenstein and Gaussian integers