Lehmer’s conjecture for matrices over the ring of integers of some imaginary quadratic fields

GD Taylor

doi:10.1016/j.jnt.2011.09.006

Lehmer’s conjecture for matrices over the ring of integers of some imaginary quadratic fields

GD Taylor

School of Mathematics

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

4 Citations (Scopus)

Abstract

Let $R=\mathcal{O}_{\Q(\sqrt{d})}$ for $d<0$, squarefree, $d\neq−1,−3$. We prove Lehmerʼs conjecture for associated reciprocal polynomials of $R$-matrices; that is, any noncyclotomic $R$-matrix has Mahler measure at least $\lambda_0=1.176\ldots$.

Translated title of the contribution	Lehmer’s conjecture for matrices over the ring of integers of some imaginary quadratic fields
Original language	English
Pages (from-to)	523-545
Number of pages	22
Journal	Journal of Number Theory
Volume	132
Issue number	4
DOIs	https://doi.org/10.1016/j.jnt.2011.09.006
Publication status	Published - Apr 2012

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@article{eb69cbfc926b4dcaa38dabe1dfeb8773,

title = "Lehmer{\textquoteright}s conjecture for matrices over the ring of integers of some imaginary quadratic fields",

abstract = "Let \$R=\textbackslash{}mathcal\{O\}\_\{\textbackslash{}Q(\textbackslash{}sqrt\{d\})\}\$ for \$d<0\$, squarefree, \$d\textbackslash{}neq−1,−3\$. We prove Lehmerʼs conjecture for associated reciprocal polynomials of \$R\$-matrices; that is, any noncyclotomic \$R\$-matrix has Mahler measure at least \$\textbackslash{}lambda\_0=1.176\textbackslash{}ldots\$.",

author = "GD Taylor",

year = "2012",

month = apr,

doi = "10.1016/j.jnt.2011.09.006",

language = "English",

volume = "132",

pages = "523--545",

journal = "Journal of Number Theory",

issn = "0022-314X",

publisher = "Academic Press Inc.",

number = "4",

}

TY - JOUR

T1 - Lehmer’s conjecture for matrices over the ring of integers of some imaginary quadratic fields

AU - Taylor, GD

PY - 2012/4

Y1 - 2012/4

N2 - Let $R=\mathcal{O}_{\Q(\sqrt{d})}$ for $d<0$, squarefree, $d\neq−1,−3$. We prove Lehmerʼs conjecture for associated reciprocal polynomials of $R$-matrices; that is, any noncyclotomic $R$-matrix has Mahler measure at least $\lambda_0=1.176\ldots$.

AB - Let $R=\mathcal{O}_{\Q(\sqrt{d})}$ for $d<0$, squarefree, $d\neq−1,−3$. We prove Lehmerʼs conjecture for associated reciprocal polynomials of $R$-matrices; that is, any noncyclotomic $R$-matrix has Mahler measure at least $\lambda_0=1.176\ldots$.

U2 - 10.1016/j.jnt.2011.09.006

DO - 10.1016/j.jnt.2011.09.006

M3 - Article (Academic Journal)

SN - 0022-314X

VL - 132

SP - 523

EP - 545

JO - Journal of Number Theory

JF - Journal of Number Theory

IS - 4

ER -

Lehmer’s conjecture for matrices over the ring of integers of some imaginary quadratic fields

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