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• catalog abstract "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.".
• catalog contributor b12015520.
• catalog contributor b12015521.
• catalog created "2001.".
• catalog date "2001".
• catalog date "2001.".
• catalog dateCopyrighted "2001.".
• catalog 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.".
• catalog description "Includes bibliographical references (p. [249]-253) and index.".
• catalog description "PHI(tau, z) and Transcendence -- Mahler's conjecture and other transcendence results -- Algebraic independence for values of Ramanujan functions -- Some remarks in proofs of algebraic independence -- Élimination multihomogène -- 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 2: Large Transcendence Degrees -- Some metric results in Transcendental Numbers Theory -- The Hilbert Nullstellensatz, Inequalities for Polynomials, and Algebraic Independence.".
• catalog extent "xiii, 256 p. ;".
• catalog hasFormat "Also available in an electronic version.".
• catalog identifier "3540414967 (softcover : alk. paper)".
• catalog isFormatOf "Also available in an electronic version.".
• catalog isPartOf "Lecture notes in mathematics, 0075-8434 ; 1752".
• catalog issued "2001".
• catalog issued "2001.".
• catalog language "eng".
• catalog publisher "Berlin ; New York : Springer,".
• catalog relation "Also available in an electronic version.".
• catalog subject "510 s 512/.73 21".
• catalog subject "Algebraic independence.".
• catalog subject "Geometry, algebraic.".
• catalog subject "Mathematics.".
• catalog subject "Number theory.".
• catalog subject "QA3 .L28 no. 1752 QA247.5".
• catalog subject "Transcendental numbers.".
• catalog tableOfContents "PHI(tau, z) and Transcendence -- Mahler's conjecture and other transcendence results -- Algebraic independence for values of Ramanujan functions -- Some remarks in proofs of algebraic independence -- Élimination multihomogène -- 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 2: Large Transcendence Degrees -- Some metric results in Transcendental Numbers Theory -- The Hilbert Nullstellensatz, Inequalities for Polynomials, and Algebraic Independence.".
• catalog title "Introduction to algebraic independence theory / Yuri V. Nesterenko, Patrice Philippon, eds. ; with contributions from: F. Amoroso ... [et al.].".
• catalog type "Computer network resources. local".
• catalog type "Electronic books. lcsh".
• catalog type "text".