On Salem numbers which are Mahler measures of nonreciprocal $2$-Pisot numbers

Toufik Zaïmi

2021/98/3-4 (12) — DOI: 10.5486/PMD.2021.8978 — pp. 467-474

On Salem numbers which are Mahler measures of nonreciprocal $2$-Pisot numbers

Authors: Toufik Zaïmi

Abstract:

Motivated by a question of D. W. Boyd, we prove a characterization of Salem numbers of degree $6$ which are Mahler measures of nonreciprocal algebraic integers, having two conjugates with modulus greater than $1$.

Keywords: Salem numbers, Mahler measure, 2-Pisot numbers

Mathematics Subject Classification: 11R06, 11R04, 11R80