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|a 9783540445500
|9 978-3-540-44550-0
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|a 10.1007/b76882
|2 doi
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|a Introduction to Algebraic Independence Theory
|h [electronic resource] /
|c edited by Yuri V. Nesterenko, Patrice Philippon.
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|a 1st ed. 2001.
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|a Berlin, Heidelberg :
|b Springer Berlin Heidelberg :
|b Imprint: Springer,
|c 2001.
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|a XVI, 260 p.
|b online resource.
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|a text
|b txt
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|a computer
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|a online resource
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|b PDF
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|a Lecture Notes in Mathematics,
|x 0075-8434 ;
|v 1752
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|a ?(?, z) and Transcendence -- Mahler's conjecture and other transcendence Results -- Algebraic independence for values of Ramanujan Functions -- Some remarks on proofs of algebraic independence -- Elimination multihomogene -- Diophantine geometry -- Géométrie diophantienne multiprojective -- Criteria for algebraic independence -- Upper bounds for (geometric) Hilbert functions -- Multiplicity estimates for solutions of algebraic differential equations -- Zero Estimates on Commutative Algebraic Groups -- Measures of algebraic independence for Mahler functions -- Algebraic Independence in Algebraic Groups. Part 1: Small Transcendence Degrees -- Algebraic Independence in Algebraic Groups. Part II: Large Transcendence Degrees -- Some metric results in Transcendental Numbers Theory -- The Hilbert Nullstellensatz, Inequalities for Polynomials, and Algebraic Independence.
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|a 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.
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|a Number theory.
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|a Algebraic geometry.
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|a Number Theory.
|0 http://scigraph.springernature.com/things/product-market-codes/M25001
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|a Algebraic Geometry.
|0 http://scigraph.springernature.com/things/product-market-codes/M11019
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|a Nesterenko, Yuri V.
|e editor.
|4 edt
|4 http://id.loc.gov/vocabulary/relators/edt
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|a Philippon, Patrice.
|e editor.
|4 edt
|4 http://id.loc.gov/vocabulary/relators/edt
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|a SpringerLink (Online service)
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|t Springer eBooks
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|i Printed edition:
|z 9783662183724
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|i Printed edition:
|z 9783540414964
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|a Lecture Notes in Mathematics,
|x 0075-8434 ;
|v 1752
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|u https://doi.org/10.1007/b76882
|z Full Text via HEAL-Link
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|a ZDB-2-SMA
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|a ZDB-2-LNM
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|a ZDB-2-BAE
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|a Mathematics and Statistics (Springer-11649)
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