On Salem half-norms

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 · · · αn , 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.