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

Gary Greaves; Graeme D Taylor

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

Gary Greaves^*
, Graeme D Taylor

^*Corresponding author for this work

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

2 Citations (Scopus)

179 Downloads (Pure)

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 atleast Lehmer's number tau(0) = 1.17628 ....

Original language	English
Article number	P42
Number of pages	22
Journal	Electronic Journal of Combinatorics
Volume	20
Issue number	1
Publication status	Published - 25 Feb 2013

Keywords

Weighted Graphs; Eigenvalues; Mahler Measure

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http://www.combinatorics.org/ojs/index.php/eljc/article/view/v20i1p42

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title = "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 atleast Lehmer's number tau(0) = 1.17628 ....",

keywords = "Weighted Graphs; Eigenvalues; Mahler Measure",

author = "Gary Greaves and Taylor, \{Graeme D\}",

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journal = "Electronic Journal of Combinatorics",

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T1 - Lehmer's conjecture for Hermitian matrices over the Eisenstein and Gaussian integers

AU - Greaves, Gary

AU - Taylor, Graeme D

PY - 2013/2/25

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N2 - 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 atleast Lehmer's number tau(0) = 1.17628 ....

AB - 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 atleast Lehmer's number tau(0) = 1.17628 ....

KW - Weighted Graphs; Eigenvalues; Mahler Measure

M3 - Article (Academic Journal)

SN - 1077-8926

VL - 20

JO - Electronic Journal of Combinatorics

JF - Electronic Journal of Combinatorics

IS - 1

M1 - P42

ER -

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

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Keywords

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