LEADER 03733nam 22005535 450 001 9910299980403321 005 20220404233613.0 010 $a88-7642-520-9 024 7 $a10.1007/978-88-7642-520-2 035 $a(CKB)3710000000359184 035 $a(EBL)1974075 035 $a(SSID)ssj0001452256 035 $a(PQKBManifestationID)11806913 035 $a(PQKBTitleCode)TC0001452256 035 $a(PQKBWorkID)11478924 035 $a(PQKB)11350840 035 $a(MiAaPQ)EBC1974075 035 $a(DE-He213)978-88-7642-520-2 035 $a(PPN)184495490 035 $a(EXLCZ)993710000000359184 100 $a20150213d2014 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aOn some applications of diophantine approximations $ea translation of C.L. Siegel?s Über einige Anwendungen diophantischer Approximationen, with a commentary by C. Fuchs and U. Zannier) /$fedited by Umberto Zannier 205 $a1st ed. 2014. 210 1$aPisa :$cScuola Normale Superiore :$cImprint: Edizioni della Normale,$d2014. 215 $a1 online resource (169 p.) 225 1 $aMonographs (Scuola Normale Superiore) ;$v2 300 $aWith a commentary and the article Integral points on curves: Siegel's theorem after Siegel's proof by Clemens Fuchs and Umberto Zannier. 311 $a88-7642-519-5 320 $aIncludes bibliographical references. 327 $aCover; Title Page; Copyright Page; Table of Contents; Preface; On some applications of Diophantine approximations; 1 Part I: On transcendental numbers; 1 Tools from complex analysis; 2 Tools from arithmetic; 3 The transcendence of J0(?); 4 Further applications of the method; 2 Part II: On Diophantine equations; 1 Equations of genus 0; 2 Ideals in function fields and number fields; 3 Equations of genus 1; 4 Auxiliary means from the theory of ABEL functions; 5 Equations of arbitrary positive genus; 6 An application of the approximation method; 7 Cubic forms with positive discriminant 327 $aÜber einige Anwendungen diophantischer ApproximationenIntegral points on curves: Siegel's theorem after Siegel's proof; 1 Introduction; 2 Some developments after Siegel's proof; 3 Siegel's Theorem and some preliminaries; 4 Three arguments for Siegel's Theorem; References; MONOGRAPHS 330 $aThis book consists mainly of the translation, by C. Fuchs, of the 1929 landmark paper "Über einige Anwendungen diophantischer Approximationen" by C.L. Siegel. The paper contains proofs of most important results in transcendence theory and diophantine analysis, notably Siegel?s celebrated theorem on integral points on algebraic curves. Many modern versions of Siegel?s proof have appeared, but none seem to faithfully reproduce all features of the original one. This translation makes Siegel?s original ideas and proofs available for the first time in English. The volume also contains the original version of the paper (in German) and an article by the translator and U. Zannier, commenting on some aspects of the evolution of this field following Siegel?s paper. To end, it presents three modern proofs of Siegel?s theorem on integral points. 410 0$aMonographs (Scuola Normale Superiore) ;$v2 606 $aNumber theory 606 $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001 615 0$aNumber theory. 615 14$aNumber Theory. 676 $a510 676 $a512.7 702 $aZannier$b Umberto$4edt$4http://id.loc.gov/vocabulary/relators/edt 906 $aBOOK 912 $a9910299980403321 996 $aOn Some Applications of Diophantine Approximations$92544386 997 $aUNINA