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

1 Citation (Scopus)

167 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

Access to Document

Full-text PDF (final published version)
This is the final published version of the article (version of record). It first appeared online via E-JC at http://www.combinatorics.org/ojs/index.php/eljc/article/view/v20i1p42. Please refer to any applicable terms of use of the publisher.
Final published version, 358 KB

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

Handle.net

Persistent link

Cite this

@article{e7923d5a6ac24c85af2b65d9db18cdf8,

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}",

year = "2013",

month = feb,

day = "25",

language = "English",

volume = "20",

journal = "Electronic Journal of Combinatorics",

issn = "1077-8926",

publisher = "Electronic Journal of Combinatorics",

number = "1",

}

TY - JOUR

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

AU - Greaves, Gary

AU - Taylor, Graeme D

PY - 2013/2/25

Y1 - 2013/2/25

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

Abstract

Keywords

Access to Document

Handle.net

Fingerprint

Cite this