03954nam 22006491 450 991046269940332120211216211404.03-11-028114-710.1515/9783110281149(CKB)2670000000432735(EBL)1130383(OCoLC)858762166(SSID)ssj0001001765(PQKBManifestationID)11532409(PQKBTitleCode)TC0001001765(PQKBWorkID)10968145(PQKB)11335298(MiAaPQ)EBC1130383(DE-B1597)175620(OCoLC)858605070(OCoLC)987673749(DE-B1597)9783110281149(Au-PeEL)EBL1130383(CaPaEBR)ebr10786153(CaONFJC)MIL807797(EXLCZ)99267000000043273520130701h20132013 uy 0engurnn#---|u||utxtccrElliptic diophantine equations /by Nikos TzanakisBerlin ;Boston :Walter de Gruyter,[2013]©20131 online resource (196 p.)De Gruyter Series in Discrete Mathematics and Applications ;2Description based upon print version of record.3-11-028091-4 Includes bibliographical references and index.Front matter --Preface --Contents --Chapter 1 Elliptic curves and equations --Chapter 2 Heights --Chapter 3 Weierstrass equations over C and R --Chapter 4 The elliptic logarithm method --Chapter 5 Linear form for the Weierstrass equation --Chapter 6 Linear form for the quartic equation --Chapter 7 Linear form for simultaneous Pell equations --Chapter 8 Linear form for the general elliptic equation --Chapter 9 Bound for the coefficients of the linear form --Chapter 10 Reducing the bound obtained in Chapter 9 --Chapter 11 S-integer solutions of Weierstrass equations --List of symbols --Bibliography --IndexThis book presents in a unified and concrete way the beautiful and deep mathematics - both theoretical and computational - on which the explicit solution of an elliptic Diophantine equation is based. It collects numerous results and methods that are scattered in the literature. Some results are hidden behind a number of routines in software packages, like Magma and Maple; professional mathematicians very often use these routines just as a black-box, having little idea about the mathematical treasure behind them. Almost 20 years have passed since the first publications on the explicit solution of elliptic Diophantine equations with the use of elliptic logarithms. The "art" of solving this type of equation has now reached its full maturity. The author is one of the main persons that contributed to the development of this art. The monograph presents a well-balanced combination of a variety of theoretical tools (from Diophantine geometry, algebraic number theory, theory of linear forms in logarithms of various forms - real/complex and p-adic elliptic - and classical complex analysis), clever computational methods and techniques (LLL algorithm and de Weger's reduction technique, AGM algorithm, Zagier's technique for computing elliptic integrals), ready-to-use computer packages. A result is the solution in practice of a large general class of Diophantine equations.De Gruyter Series in Discrete Mathematics and ApplicationsDiophantine equationsElliptic functionsElectronic books.Diophantine equations.Elliptic functions.512.7/2Tzanakis Nikos1952-1056020MiAaPQMiAaPQMiAaPQBOOK9910462699403321Elliptic diophantine equations2490036UNINA01140nam0 22002891i 450 UON0048875820231205105322.88927-07-31134-020180525d1987 |0itac50 bafreFR|||| |||||ˆLa ‰force de la regleWittgenstein et l'invention de la necessiteJacques BouveresseParisLes editions de Minuit1987175 p.23 cm.001UON003486512001 Critique210 ParisLes Éditions de Minuit.WITTGENSTEIN LUDWIGUONC036356FIFRParisUONL002984199.49Filosofia occidentale. Europa.21BouveresseJacquesUONV060452160307Les Éditions de MinuitUONV254617650ITSOL20250606RICASIBA - SISTEMA BIBLIOTECARIO DI ATENEOUONSIUON00488758SIBA - SISTEMA BIBLIOTECARIO DI ATENEOSI FS 07187 SI FP 15119 5 Force de la règle1703467UNIOR