Algebraic integers with two conjugates outside the unit circle

Abstract

In this paper we consider algebraic integers, θ, such that θ and θ¯ (θ ╪ θ¯) are the only algebraic conjugates of θ that lie outside the unit circle.Let S1 be the set of algebraic integers, ρ, necessarily real, all of whose conjugates, except ρ, satisfy | z < 1.

Representations for complex numbers with integer digits

“…Algebraic results on complex Pisot numbers can be found in [10,22,62]. Some basic properties of complex Salem numbers have been studied in [52] (without using the term complex Salem number).…”

Seventy years of Salem numbers

“…For generalisations of Salem numbers, see Bertin [7,8], Cantor [30], Kerada [59], Meyer [85], Samet [102], Schreiber [105] and Smyth [110]. Note the correction made to [102] in [110]. See also Section 4.1 below for 2-Salem numbers.…”

The growth function of Coxeter dominoes and 2–Salem numbers

“…In this paper, we focus on a 2-Salem number. Note that Samet [17] also defined a set of algebraic integers corresponding to 2-Salem numbers.…”