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

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Algebraic Independencere 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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0072-7830 k deals with values of the usual exponential function e^z. A central open problem is the conjecture on algebraic independence of logarithms of algebraic numbers. This book includes proofs of the main basic results (theorems of Hermite-Lindemann, Gelfond-Schneider, 6 exponentials theorem), an introdu

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https://doi.org/10.1007/978-3-319-14738-3.,...,..) then we can estimate from below |.(..,...,..)|. The lower bound will depend upon the degrees of . with respect to each of the X.’s, the absolute values of its coefficients as well as some measure of the ..’s.

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