Some metric results in Transcendental Numbers Theory

Abstract

In this Chapter we describe some results in the metric theory of transcendental numbers. Let begin with some notation. If P ∈ Z[x[inl, ⋯, x _m] is a non - zero polynomial, we define its size t(P) as h(P) + deg (P). Here, h(P) is the Weil’s logarithmic height of P (so, if the ged of the coefficients of P is 1, then h(P) is the logarithm of the maximum module of the coefficients of P) and deg (P) is the total degree of P. Let α = (α₁,⋯, α_m) ∈ C^m with α₁,⋯, α_m algebraically dependent: we define t(α) as the minimum size of a non - zero polynomial P ∈ Z[x _l⋯,x _m] such that P(α) = 0. er’s author : Francesco AMOROSO.