Geodesic
Lehmer's conjecture for Hermitian matrices over the Eisenstein and Gaussian integers
Graeme Taylor1 ; Gary Greaves2
1Heilbronn Institute for Mathematical Research, University of Bristol.
2Graduate School of Information Sciences, Tohoku University.
The electronic journal of combinatorics, Tome 20 (2013) no. 1
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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 $\tau_0 = 1.17628\dots$.
DOI : 10.37236/2834
Classification : 05C22, 05C50, 15B57, 15B33
Mots-clés : weighted graphs, eigenvalues, Mahler measure

Graeme Taylor  1   ; Gary Greaves  2

1 Heilbronn Institute for Mathematical Research, University of Bristol.
2 Graduate School of Information Sciences, Tohoku University. 
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     author = {Graeme Taylor and Gary Greaves},
     title = {Lehmer's conjecture for {Hermitian} matrices over the {Eisenstein} and {Gaussian} integers},
     journal = {The electronic journal of combinatorics},
     year = {2013},
     volume = {20},
     number = {1},
     doi = {10.37236/2834},
     zbl = {1267.05137},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/2834/}
}
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Graeme Taylor; Gary Greaves. Lehmer's conjecture for Hermitian matrices over the Eisenstein and Gaussian integers. The electronic journal of combinatorics, Tome 20 (2013) no. 1. doi: 10.37236/2834

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