On algebraic integers which are 2-Salem elements in positive characteristic

Abstract

Bateman and Duquette have initiated the study of Salem elements in positive characteristic. Later, Kerada introduced and studied j-Salem numbers ([Formula: see text]). To complete this circle of ideas we introduce 2-Salem elements over the field of formal Laurent series over a finite field [Formula: see text]. We extend the above-cited studies and we provide some analog results. The main result of this note is Theorem 1.2 which characterizes the set [Formula: see text] of 2-Salem series when [Formula: see text].