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

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书目名称Introduction to Algebraic Independence Theory
编辑Yuri V. Nesterenko,Patrice Philippon
视频videohttp://file.papertrans.cn/474/473393/473393.mp4
概述The first didactically-conceived presentation of the recent development in transcendence theory.Includes supplementary material:
丛书名称Lecture Notes in Mathematics
图书封面Titlebook: Introduction to Algebraic Independence Theory; Yuri V. Nesterenko,Patrice Philippon Book 2001 Springer-Verlag Berlin Heidelberg 2001 Algeb
描述In the last five years there has been very significant progress in the development of transcendence theory. A new approach to the arithmetic properties of values of modular forms and theta-functions was found. The solution of the Mahler-Manin problem on values of modular function j(tau) and algebraic independence of numbers pi and e^(pi) are most impressive results of this breakthrough. The book presents these and other results on algebraic independence of numbers and further, a detailed exposition of methods created in last the 25 years, during which commutative algebra and algebraic geometry exerted strong catalytic influence on the development of the subject.
出版日期Book 2001
关键词Algebraic independence; Dimension; algebra; algebraic geometry; algebraic group; commutative algebra; elim
版次1
doihttps://doi.org/10.1007/b76882
isbn_softcover978-3-540-41496-4
isbn_ebook978-3-540-44550-0Series ISSN 0075-8434 Series E-ISSN 1617-9692
issn_series 0075-8434
copyrightSpringer-Verlag Berlin Heidelberg 2001
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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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