Lehmer's conjecture for Hermitian matrices over the Eisenstein and Gaussian integers
classification
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keywords
lehmereisensteingaussianhermitianintegersmatricespolynomialsarising
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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... .
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