03689nam 22006135 450 99646637950331620200704042726.03-540-44550-110.1007/b76882(CKB)1000000000233190(SSID)ssj0000324152(PQKBManifestationID)12091422(PQKBTitleCode)TC0000324152(PQKBWorkID)10312910(PQKB)10620013(DE-He213)978-3-540-44550-0(MiAaPQ)EBC3073218(PPN)155220160(EXLCZ)99100000000023319020121227d2001 u| 0engurnn|008mamaatxtccrIntroduction to Algebraic Independence Theory[electronic resource] /edited by Yuri V. Nesterenko, Patrice Philippon1st ed. 2001.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2001.1 online resource (XVI, 260 p.) Lecture Notes in Mathematics,0075-8434 ;1752Bibliographic Level Mode of Issuance: Monograph3-540-41496-7 Includes bibliographical references and index.?(?, 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.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.Lecture Notes in Mathematics,0075-8434 ;1752Number theoryAlgebraic geometryNumber Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M25001Algebraic Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M11019Number theory.Algebraic geometry.Number Theory.Algebraic Geometry.512/.73Nesterenko Yuri Vedthttp://id.loc.gov/vocabulary/relators/edtPhilippon Patriceedthttp://id.loc.gov/vocabulary/relators/edtMiAaPQMiAaPQMiAaPQBOOK996466379503316Introduction to algebraic independence theory262226UNISA