Mahler measure of a difference of two conjugates*

Abstract

Suppose that an algebraic number β of degree d = n(n − 1) over ℚ is expressible by the difference of two conjugate algebraic integers α1 ≠ α2 of degree n, namely, β = α1− α2. We prove that then there exists a constant c > 1, which depends on \( \overline{\mid \alpha \mid } \) = max1≤i≤n ∣αi∣ only, such that M(β)1/d > c.