LEADER 03689nam 22006135 450 001 996466379503316 005 20200704042726.0 010 $a3-540-44550-1 024 7 $a10.1007/b76882 035 $a(CKB)1000000000233190 035 $a(SSID)ssj0000324152 035 $a(PQKBManifestationID)12091422 035 $a(PQKBTitleCode)TC0000324152 035 $a(PQKBWorkID)10312910 035 $a(PQKB)10620013 035 $a(DE-He213)978-3-540-44550-0 035 $a(MiAaPQ)EBC3073218 035 $a(PPN)155220160 035 $a(EXLCZ)991000000000233190 100 $a20121227d2001 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aIntroduction to Algebraic Independence Theory$b[electronic resource] /$fedited by Yuri V. Nesterenko, Patrice Philippon 205 $a1st ed. 2001. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2001. 215 $a1 online resource (XVI, 260 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1752 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-41496-7 320 $aIncludes bibliographical references and index. 327 $a?(?, 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. 330 $aIn the last five years there has been very significant progress in the development of transcendence theory. A new approach to the arithmetic properties of values of modular forms and theta-functions was found. The solution of the Mahler-Manin problem on values of modular function j(tau) and algebraic independence of numbers pi and e^(pi) are most impressive results of this breakthrough. The book presents these and other results on algebraic independence of numbers and further, a detailed exposition of methods created in last the 25 years, during which commutative algebra and algebraic geometry exerted strong catalytic influence on the development of the subject. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1752 606 $aNumber theory 606 $aAlgebraic geometry 606 $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001 606 $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019 615 0$aNumber theory. 615 0$aAlgebraic geometry. 615 14$aNumber Theory. 615 24$aAlgebraic Geometry. 676 $a512/.73 702 $aNesterenko$b Yuri V$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aPhilippon$b Patrice$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466379503316 996 $aIntroduction to algebraic independence theory$9262226 997 $aUNISA