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Introduction to Algebraic Independence Theory

Introduction to Algebraic Independence Theory
Catalogue Information
Field name Details
Dewey Class 512.7
Title Introduction to Algebraic Independence Theory ([EBook] /) / edited by Yuri V. Nesterenko, Patrice Philippon.
Added Personal Name Nesterenko, Yuri V. editor.
Philippon, Patrice editor.
Other name(s) SpringerLink (Online service)
Publication Berlin, Heidelberg : : Springer Berlin Heidelberg, , 2001.
Physical Details XVI, 260 p. : online resource.
Series Lecture Notes in Mathematics 0075-8434 ; ; 1752
ISBN 9783540445500
Summary Note 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.:
Contents note ?(?, 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.
System details note Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
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