# 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 contribution Lehmer’s conjecture for matrices over the ring of integers of some imaginary quadratic fields English 523-545 22 Journal of Number Theory 132 4 https://doi.org/10.1016/j.jnt.2011.09.006 Published - Apr 2012