LEADER 03954nam 22006491 450 001 9910462699403321 005 20211216211404.0 010 $a3-11-028114-7 024 7 $a10.1515/9783110281149 035 $a(CKB)2670000000432735 035 $a(EBL)1130383 035 $a(OCoLC)858762166 035 $a(SSID)ssj0001001765 035 $a(PQKBManifestationID)11532409 035 $a(PQKBTitleCode)TC0001001765 035 $a(PQKBWorkID)10968145 035 $a(PQKB)11335298 035 $a(MiAaPQ)EBC1130383 035 $a(DE-B1597)175620 035 $a(OCoLC)858605070 035 $a(OCoLC)987673749 035 $a(DE-B1597)9783110281149 035 $a(Au-PeEL)EBL1130383 035 $a(CaPaEBR)ebr10786153 035 $a(CaONFJC)MIL807797 035 $a(EXLCZ)992670000000432735 100 $a20130701h20132013 uy 0 101 0 $aeng 135 $aurnn#---|u||u 181 $ctxt 182 $cc 183 $acr 200 10$aElliptic diophantine equations /$fby Nikos Tzanakis 210 1$aBerlin ;$aBoston :$cWalter de Gruyter,$d[2013] 210 4$dİ2013 215 $a1 online resource (196 p.) 225 0 $aDe Gruyter Series in Discrete Mathematics and Applications ;$v2 300 $aDescription based upon print version of record. 311 0 $a3-11-028091-4 320 $aIncludes bibliographical references and index. 327 $tFront matter --$tPreface --$tContents --$tChapter 1 Elliptic curves and equations --$tChapter 2 Heights --$tChapter 3 Weierstrass equations over C and R --$tChapter 4 The elliptic logarithm method --$tChapter 5 Linear form for the Weierstrass equation --$tChapter 6 Linear form for the quartic equation --$tChapter 7 Linear form for simultaneous Pell equations --$tChapter 8 Linear form for the general elliptic equation --$tChapter 9 Bound for the coefficients of the linear form --$tChapter 10 Reducing the bound obtained in Chapter 9 --$tChapter 11 S-integer solutions of Weierstrass equations --$tList of symbols --$tBibliography --$tIndex 330 $aThis book presents in a unified and concrete way the beautiful and deep mathematics - both theoretical and computational - on which the explicit solution of an elliptic Diophantine equation is based. It collects numerous results and methods that are scattered in the literature. Some results are hidden behind a number of routines in software packages, like Magma and Maple; professional mathematicians very often use these routines just as a black-box, having little idea about the mathematical treasure behind them. Almost 20 years have passed since the first publications on the explicit solution of elliptic Diophantine equations with the use of elliptic logarithms. The "art" of solving this type of equation has now reached its full maturity. The author is one of the main persons that contributed to the development of this art. The monograph presents a well-balanced combination of a variety of theoretical tools (from Diophantine geometry, algebraic number theory, theory of linear forms in logarithms of various forms - real/complex and p-adic elliptic - and classical complex analysis), clever computational methods and techniques (LLL algorithm and de Weger's reduction technique, AGM algorithm, Zagier's technique for computing elliptic integrals), ready-to-use computer packages. A result is the solution in practice of a large general class of Diophantine equations. 410 3$aDe Gruyter Series in Discrete Mathematics and Applications 606 $aDiophantine equations 606 $aElliptic functions 608 $aElectronic books. 615 0$aDiophantine equations. 615 0$aElliptic functions. 676 $a512.7/2 700 $aTzanakis$b Nikos$f1952-$01056020 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910462699403321 996 $aElliptic diophantine equations$92490036 997 $aUNINA