Salem numbers as Mahler measures of nonreciprocal units

Tom 176 / 2016

Artūras Dubickas Acta Arithmetica 176 (2016), 81-88 MSC: Primary 11R09; Secondary 11R06, 11R32. DOI: 10.4064/aa8407-8-2016 Opublikowany online: 10 October 2016


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.


  • Artūras DubickasDepartment of Mathematics and Informatics
    Vilnius University
    Naugarduko 24
    Vilnius LT-03225, Lithuania

Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Przepisz kod z obrazka

Odśwież obrazek

Odśwież obrazek