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

GD Taylor

Research output: Contribution to journalArticle (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 contributionLehmer’s conjecture for matrices over the ring of integers of some imaginary quadratic fields
Original languageEnglish
Pages (from-to)523-545
Number of pages22
JournalJournal of Number Theory
Volume132
Issue number4
DOIs
Publication statusPublished - Apr 2012

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