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＜電子ブック＞
Introduction to Algebraic Independence Theory / edited by Yuri V. Nesterenko, Patrice Philippon
(Lecture Notes in Mathematics. ISSN:16179692 ; 1752)

版	1st ed. 2001.
出版者	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
出版年	2001
本文言語	英語
大きさ	XVI, 260 p : online resource
冊子体	Introduction to algebraic independence theory / Yuri V. Nesterenko, Patrice Philippon (eds.) ; with contributions from, F. Amoroso ... [et al.]
著者標目	Nesterenko, Yuri V editor Philippon, Patrice editor SpringerLink (Online service)
件　名	LCSH:Number theory LCSH:Algebraic geometry FREE:Number Theory FREE:Algebraic Geometry
一般注記	?(?, 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 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 Accessibility summary: This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format Inaccessible, or known limited accessibility No reading system accessibility options actively disabled Publisher contact for further accessibility information: accessibilitysupport@springernature.com HTTP:URL=https://doi.org/10.1007/b76882

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