Chapter

Introduction to Algebraic Independence Theory

Volume 1752 of the series Lecture Notes in Mathematics pp 227-237

Date:

Some metric results in Transcendental Numbers Theory

* Final gross prices may vary according to local VAT.

Get Access

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,⋯, αm) ∈ Cm with α1,⋯, αm 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.