Introduction to Algebraic Independence Theory [electronic resource] /

Nesterenko, Yuri V. editor.; Philippon, Patrice. editor.; SpringerLink (Online service)

Introduction to Algebraic Independence Theory [electronic resource] /

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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Main Authors:	Nesterenko, Yuri V. editor., Philippon, Patrice. editor., SpringerLink (Online service)
Format:	Texto biblioteca
Language:	eng
Published:	Berlin, Heidelberg : Springer Berlin Heidelberg, 2001
Subjects:	Mathematics., Algebraic geometry., Number theory., Number Theory., Algebraic Geometry.,
Online Access:	http://dx.doi.org/10.1007/b76882
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spelling	KOHA-OAI-TEST:2081692018-07-30T23:38:51ZIntroduction to Algebraic Independence Theory [electronic resource] / Nesterenko, Yuri V. editor. Philippon, Patrice. editor. SpringerLink (Online service) textBerlin, Heidelberg : Springer Berlin Heidelberg,2001.engIn 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.?(?, 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.Mathematics.Algebraic geometry.Number theory.Mathematics.Number Theory.Algebraic Geometry.Springer eBookshttp://dx.doi.org/10.1007/b76882URN:ISBN:9783540445500
institution	COLPOS
collection	Koha
country	México
countrycode	MX
component	Bibliográfico
access	En linea En linea
databasecode	cat-colpos
tag	biblioteca
region	America del Norte
libraryname	Departamento de documentación y biblioteca de COLPOS
language	eng
topic	Mathematics. Algebraic geometry. Number theory. Mathematics. Number Theory. Algebraic Geometry. Mathematics. Algebraic geometry. Number theory. Mathematics. Number Theory. Algebraic Geometry.
spellingShingle	Mathematics. Algebraic geometry. Number theory. Mathematics. Number Theory. Algebraic Geometry. Mathematics. Algebraic geometry. Number theory. Mathematics. Number Theory. Algebraic Geometry. Nesterenko, Yuri V. editor. Philippon, Patrice. editor. SpringerLink (Online service) Introduction to Algebraic Independence Theory [electronic resource] /
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.
format	Texto
topic_facet	Mathematics. Algebraic geometry. Number theory. Mathematics. Number Theory. Algebraic Geometry.
author	Nesterenko, Yuri V. editor. Philippon, Patrice. editor. SpringerLink (Online service)
author_facet	Nesterenko, Yuri V. editor. Philippon, Patrice. editor. SpringerLink (Online service)
author_sort	Nesterenko, Yuri V. editor.
title	Introduction to Algebraic Independence Theory [electronic resource] /
title_short	Introduction to Algebraic Independence Theory [electronic resource] /
title_full	Introduction to Algebraic Independence Theory [electronic resource] /
title_fullStr	Introduction to Algebraic Independence Theory [electronic resource] /
title_full_unstemmed	Introduction to Algebraic Independence Theory [electronic resource] /
title_sort	introduction to algebraic independence theory [electronic resource] /
publisher	Berlin, Heidelberg : Springer Berlin Heidelberg,
publishDate	2001
url	http://dx.doi.org/10.1007/b76882
work_keys_str_mv	AT nesterenkoyuriveditor introductiontoalgebraicindependencetheoryelectronicresource AT philipponpatriceeditor introductiontoalgebraicindependencetheoryelectronicresource AT springerlinkonlineservice introductiontoalgebraicindependencetheoryelectronicresource
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Introduction to Algebraic Independence Theory [electronic resource] /

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