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[null,"1.","Record Nr.",null,"UNISA996466379503316"]
[null,null,"Titolo",null,"Introduction to Algebraic Independence Theory [[electronic resource] /] / edited by Yuri V. Nesterenko, Patrice Philippon"]
[null,null,"Pubbl/distr/stampa",null,"Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2001"]
[null,null,"ISBN",null,"3-540-44550-1"]
[null,null,"Edizione",null,"[1st ed. 2001.]"]
[null,null,"Descrizione fisica",null,"1 online resource (XVI, 260 p.)"]
[null,null,"Collana",null,"Lecture Notes in Mathematics, , 0075-8434 ; ; 1752"]
[null,null,"Disciplina",null,"512/.73"]
[null,null,"Soggetti",null,"Number theory"]
[{"$nulls":4},"Algebraic geometry"]
[{"$nulls":4},"Number Theory"]
[{"$nulls":4},"Algebraic Geometry"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Note generali","Bibliographic Level Mode of Issuance: Monograph"]
[null,null,null,"Nota di bibliografia","Includes bibliographical references and index."]
[null,null,"Nota di contenuto",null,"?(?, z) and Transcendence -- Mahler’s conjecture and other transcendence Results -- Algebraic independence for values of Ramanujan Functions -- Some remarks on proofs of algebraic independence -- Elimination multihomogene -- Diophantine geometry -- Géométrie diophantienne multiprojective -- Criteria for algebraic independence -- Upper bounds for (geometric) Hilbert functions -- Multiplicity estimates for solutions of algebraic differential equations -- Zero Estimates on Commutative Algebraic Groups -- Measures of algebraic independence for Mahler functions -- Algebraic Independence in Algebraic Groups. Part 1: Small Transcendence Degrees -- Algebraic Independence in Algebraic Groups. Part II: Large Transcendence Degrees -- Some metric results in Transcendental Numbers Theory -- The Hilbert Nullstellensatz, Inequalities for Polynomials, and Algebraic Independence."]
[null,null,null,"Sommario/riassunto","In the last five years there has been very significant progress in the development of transcendence theory. A new approach to the arithmetic properties of values of modular forms and theta-functions was found. The solution of the Mahler-Manin problem on values of modular function j(tau) and algebraic independence of numbers pi and e^(pi) are most impressive results of this breakthrough. The book presents these and other results on algebraic independence of numbers and further, a detailed exposition of methods created in last the 25 "]
[{"$nulls":4},"years, during which commutative algebra and algebraic geometry exerted strong catalytic influence on the development of the subject."]