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

  • Graeme Taylor
  • Gary Greaves
DOI: https://doi.org/10.37236/2834
Keywords: Weighted Graphs, Eigenvalues, Mahler Measure

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 $\tau_0 = 1.17628\dots$.
Published
2013-02-25
How to Cite
Taylor, G., & Greaves, G. (2013). Lehmer’s Conjecture for Hermitian Matrices over the Eisenstein and Gaussian Integers. The Electronic Journal of Combinatorics, 20(1), P42. https://doi.org/10.37236/2834
Issue
Volume 20, Issue 1 (2013)
Article Number
P42