Titlebook: Introduction to Algebraic Independence Theory; Yuri V. Nesterenko,Patrice Philippon Book 2001 Springer-Verlag Berlin Heidelberg 2001 Algeb

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Multiplicity estimates for solutions of algebraic differential equations,.) ε .[. .,?, . .], such that deg., . ≤., deg. . ≤. and . The upper bounds for this order of zero in terms of n and h depends on individual properties of functions . ., ?, . .. For example, if functions are algebraically dependent over .(.), and . is a polynomial which realise the dependence we have

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Algebraic Independence in Algebraic Groups. Part 1: Small Transcendence Degrees,braic groups. We consider only small transcendence degrees, by which we mean results asserting the algebraic independence of at least two numbers belonging to some set of numbers typically defined as values of the exponential map of some commutative algebraic group. Even in this special case, a sing

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