4 research outputs found
Lower Bounds for Heights in Relative Galois Extensions
The goal of this paper is to obtain lower bounds on the height of an
algebraic number in a relative setting, extending previous work of Amoroso and
Masser. Specifically, in our first theorem we obtain an effective bound for the
height of an algebraic number when the base field is a
number field and is Galois. Our second result
establishes an explicit height bound for any non-zero element which is
not a root of unity in a Galois extension , depending on
the degree of and the number of conjugates of
which are multiplicatively independent over . As a consequence, we
obtain a height bound for such that is independent of the
multiplicative independence condition