Introduction to Algebraic Independence Theory pp 227-237

Part of the Lecture Notes in Mathematics book series (LNM, volume 1752)

Some metric results in Transcendental Numbers Theory



In this Chapter we describe some results in the metric theory of transcendental numbers. Let begin with some notation. If P ∈ Z[x[inl, ⋯, xm] 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[xl⋯,xm] such that P(α) = 0. er’s author : Francesco AMOROSO.


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© Springer-Verlag Berlin Heidelberg 2001

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