Research Article

On Salem half-norms

Published in: Quaestiones Mathematicae
Volume 45 , issue 1 , 2022 , pages: 91–99

DOI: 10.2989/16073606.2020.1848938

Author(s): Toufik Zaïmi , Saudi Arabia

Keywords: 11R06 , 11R09 , 11R80 , 12D10 , 11R06 , 11R09 , 11R80 , 12D10

Abstract

Let α be a Salem number with conjugates , where α ₁ := α. We prove some properties of the products of the form α ₁ α ₂ · · · α_n , called, by A. Dubickas and C.J. Smyth, Salem half-norms. This allows us to complete, partially, two related results due to C. Christopoulos and J. McKee about the Galois group of the splitting field of the minimal polynomial of α, and to A. Dubickas on a question of D.W. Boyd about Salem numbers which are Mahler measures of non-reciprocal algebraic integers.

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