Introduction to Algebraic Independence Theory [[electronic resource] /] / edited by Yuri V. Nesterenko, Patrice Philippon

• Pubblicazione: Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2001
• Edizione: 1st ed. 2001.
• Descrizione fisica: 1 online resource (XVI, 260 p.)
• Disciplina: 512/.73
• Soggetto topico: Number theory; Algebraic geometry; Number Theory; Algebraic Geometry
• Persona (resp. second.): NesterenkoYuri V; PhilipponPatrice
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: ?(?, 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.
• Sommario/riassunto: 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.
• Titolo autorizzato: Introduction to algebraic independence theory
• ISBN: 3-540-44550-1
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 996466379503316
• Lo trovi qui: Univ. di Salerno
• Serie: Lecture Notes in Mathematics, . 0075-8434 ; ; 1752