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OverviewFull Product DetailsAuthor: Yuri V. Nesterenko , F. Amoroso , Patrice Philippon , D. BertrandPublisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K Edition: 2001 ed. Volume: 1752 Dimensions: Width: 15.50cm , Height: 1.40cm , Length: 23.50cm Weight: 0.860kg ISBN: 9783540414964ISBN 10: 3540414967 Pages: 260 Publication Date: 18 January 2001 Audience: College/higher education , Professional and scholarly , Postgraduate, Research & Scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsPreface List of Contributors Chapter 1. PHI (tau,z) and Transcendence 1. Differential rings and modular forms 2. Explicit differential equations 3. Singular values 4. Transcendence on phi and z Chapter 2. Mahler's conjecture and other transcendence results 1. Introduction 2. A proof of Mahler's conjecture 3. K. Barre's work on modular functions 4. Conjectures about modular and exponential functions Chapter 3. Algebraic independence for values of Ramanujan functions 1. Main theorem and consequences 2. How it can be proved? 3. Constructions of the sequence of polynomials 4. Algebraic fundamentals 5. Another proof of Theorem 1.1 Chapter 4. Some remarks on proofs of algebraic independence 1. Connection with elliptic functions 2. Connection with modular series 3. Another proof of algebraic independence of phi, ephi and TAU ( 1/4) 4. Approximation properties Chapter 5. Elimination multihomogene 1. Introduction 2. Formes eliminantes des ideaux multihomogenes 3. Formes resultantes des ideaux multihomogenes Chapter 6. Diophantine geometry 1. Elimination theory 2. Degree 3. Height 4. Geometric and arithmetic Bezout theorems 5. Distance from a point to a variety 6. Auxiliary results 7. First metric Bezout theorem 8. Second metric Bezout theorem Chapter 7. Geometrie diophantienne multiprojective 1. Introduction 2. Hauteurs 3. Une formule d'intersection 4. Distances Chapter 8. Criteria for algebraic independence 1. Criteria for algebraic independence 2. Mixed Segre- Veronese embeddings 3. Multi-projective criteria for algebraic independence Chapter 9. Upper bounds for (geometric ) Hilbert functions 1. The absolute case (following Kollar) 2. The relative case Chapter 10. Multiplicity estimates for solutions of algebraic differential equations 1. Introduction 2. Reduction of Theorem 1.1 tobounds for polynomial ideals 3. Auxiliary assertions 4. End of the proof of Theorem 2.2 5. D-property for Ramanujan functions Chapter 11. Zero Estimates on Commutative Algebraic Groups 1. Introduction 2. Degree of an intersection on an algebraic group 3. Translation and derivations 4. Statement and proof of the zero estimate Chapter 12. Measures of algebraic independence for Mahler functions 1. Theorems 2. Proof of main theorem 3. Proof of multiplicity estimate Chapter 13. Algebraic Independence in Algebraic Groups. Part 1: Small Transcendence Degrees 1. Introduction 2. General statements 3. Concrete applications 4. A criteria of algebraic independence with multiplicities 5. Introducing a matrix M 6. The rank of the matrix M 7. Analytic upper bound 8. Proof of Proposition 5.1 Chapter 14. Algebraic Independence in Algebraic Groups. Part 2: Large Transcendence Degrees 1. Introduction 2. Conjectures 3. Proofs Chapter 15. Some metric results in Transcendental Numbers Theory 1. Introduction 2. One dimensional results 3. Several dimensional results: 'comparison Theorem' 4. Several dimensional results: proof of Chudnovsky's conjecture Chapter 16. The Hilbert Nullstellensatz, Inequalities for Polynomials, and Algebraic Independence 1. The Hilbert Nullstellensatz and Effectivity 2. Liouville-Lojasiewicz Inequality 3. The Lojasiewicz Inequality Implies the Nullstellensatz 4. Geometric Version of the Nullstellensatz or Irrelevance of the Nullstellen Inequality for the Nullstellensatz 5. Arithmetic Aspects of the Bezout Version 6. Some Algorithmic Aspects of the Bezout Version Bibliography IndexReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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