Titlebook: G-Functions and Geometry; A Publication of the Yves André Book 1989 Springer Fachmedien Wiesbaden 1989 Algebra.Arithmetik.Differentialgleic

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978-3-528-06317-7Springer Fachmedien Wiesbaden 1989

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G-Functions and Geometry978-3-663-14108-2Series ISSN 0179-2156

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0179-2156 Overview: 978-3-528-06317-7978-3-663-14108-2Series ISSN 0179-2156

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Introductionitute a new topic: they were brought in by C.L.Siegel in 1929, in his famous paper on applications of diophantine approximation. He defined G-functions to be the formal power series y = Σa.x. whose coefficients a lie in some algebraic number field K , which fulfill the following three conditions:

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meditation

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Independence of Values of G-Functionsniques he found (and described in the same paper) for studying the diophantine approximation properties of values of what he called E-functions. However no proof had appeared, and the first attempt in the direction of Siegel’s statements was in M.S. Numagomedov’s work, more than fourty years later.

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Towards Grothendieck’s Conjecture on Periods of Algebraic Manifolds? among the periods of an (algebraic) projective manifold X defined over Φ? is determined by the Hodge cycles on the powers of X. (or by the algebraic cycles, in the strongest version). Building upon methods of chapter VII and of variation of Hodge structure, we give a partial answer to this conject

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