Instytut Matematyczny Polskiej Akademii Nauk / pl / Wydawnictwa / Czasopisma IMPAN / Acta Arithmetica / Wszystkie zeszyty

Streszczenie

We show that for $d=4$ and for each $d=4\ell+2$, where $\ell \in \mathbb N$, there are Salem numbers of degree $d$ which belong to the set of nonreciprocal Mahler measures $L_0$. In passing, we show that for every odd $n$ there exist Salem polynomials $f$ of degree $d=2n$ whose Galois group is isomorphic to $\mathbb Z_2^{n-1}\rtimes G_g$, where $G_g$ is the Galois group of the trace polynomial $g$ of $f$. The first result addresses a corresponding question of Boyd, whereas the second result is related to and in some sense completes an earlier result of Christopoulos and McKee.