Titlebook: Diophantine Approximation on Linear Algebraic Groups; Transcendence Proper Michel Waldschmidt Book 2000 Springer-Verlag Berlin Heidelberg 2

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M. Jansen,M. Judas,J. Saborowskire algebraic numbers . such that |.|is small but not zero. One deduces that numbers ..,..., .. belonging to a field of transcendence degree 1 admit good simultaneous approximations by algebraic numbers ..,..., .., where the quality of the approximation, namely the number max.... |.. ? ..|, is controlled in terms of the degree [?(..,..., ..): ?].

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https://doi.org/10.1007/978-3-662-11569-5Algebra; Diophantine approximation; Exponential Functions; Linear Algebraic groups; Measures of Independ

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Michel WaldschmidtIncludes supplementary material:

Chronological

Grundlehren der mathematischen Wissenschaftenhttp://image.papertrans.cn/e/image/280537.jpg

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Design Principles for Micro Modelsas well as in the nonhomogeneous version. We also describe the six exponentials Theorem, we present the state of the art on the problem of algebraic independence of logarithms of algebraic numbers. We conclude with a few comments on the Linear Subgroup Theorem.

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Robert Tanton,Kimberley L. Edwardsle. Our aim is to prove the theorems of Hermite-Lindemann and Gel’ fond-Schneider by means of the alternants or interpolation determinants of M. Laurent [Lau 1989]. The real case of these two theorems (§§ 2.3 and 2.4) is easier, thanks to an estimate, due to G. Pólya (Lemma 2.2), for the number of r

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