Lehmer's Conjecture for Hermitian Matrices over the Eisenstein and Gaussian Integers

Graeme Taylor, Gary Greaves

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 $\tau_0 = 1.17628\dots$.

Keywords


Weighted Graphs; Eigenvalues; Mahler Measure

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