Introduction to Algebraic Independence Theory by Yuri V. Nesterenko (English) Pa

The Nile on eBay   FREE SHIPPING UK WIDE   Introduction to Algebraic Independence Theory by Yuri V. Nesterenko, F. Amoroso, D. Bertrand, Patrice Philippon, W.D. Brownawell, G. Diaz, M. Laurent, YU.V. Nesterenko, K. Nishioka

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.

FORMATPaperback LANGUAGEEnglish CONDITIONBrand New Publisher Description

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.

Notes

The first didactically-conceived presentation of the recent development in transcendence theory

Table of Contents

?(?, 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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Long Description

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.

Feature

The first didactically-conceived presentation of the recent development in transcendence theory

Details ISBN3540414967 Short Title INTRO TO ALGEBRAIC INDEPENDENC Language English ISBN-10 3540414967 ISBN-13 9783540414964 Media Book Format Paperback Series Number 1752 Year 2001 Imprint Springer-Verlag Berlin and Heidelberg GmbH & Co. K Place of Publication Berlin Country of Publication Germany Edited by Yuri V. Nesterenko Pages 260 Illustrations XVI, 260 p. DOI 10.1007/b76882;10.1007/978-3-540-44550-0 Author K. Nishioka Publisher Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Edition Description 2001 ed. Series Lecture Notes in Mathematics Edition 2001st Publication Date 2001-01-18 DEWEY 512 Audience Postgraduate, Research & Scholarly We've got this

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