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

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

2011-03-23

arxiv.org/abs/1103.4579v1

Mathematics

Number Theory

Scientific paper

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

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