A+ CATEGORY SCIENTIFIC UNIT

PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

Salem numbers as Mahler measures of nonreciprocal units

Volume 176 / 2016

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

Abstract

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.

Authors

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

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image