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1998-1999 | 87 | 4 | 339-365
Tytuł artykułu

Solving elliptic diophantine equations: the general cubic case

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Warianty tytułu
Języki publikacji
EN
Abstrakty
Twórcy
  • Econometric Institute, Erasmus University, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands
  • Sportsingel 30, 2924 XN Krimpen aan den IJssel, The Netherlands
Bibliografia
  • [BC70] A. Baker and J. Coates, Integer points on curves of genus 1, Proc. Cambridge Philos. Soc. 67 (1970), 595-602.
  • [BH96] Yu. Bilu and G. Hanrot, Solving Thue equations of high degree, J. Number Theory 60 (1996), 373-392.
  • [BH98] Yu. Bilu and G. Hanrot, Solving superelliptic diophantine equations by Baker's method, Compositio Math. 112 (1998), 273-312.
  • [BST97] A. Bremner, R. J. Stroeker and N. Tzanakis, On sums of consecutive squares, J. Number Theory 62 (1997), 39-70.
  • [Co97] I. Connell, Elliptic Curve Handbook, available from the ftp site of McGill University in the directory math.mcgill.ca/pub/ECH1. From the same site the Apecs package can be downloaded.
  • [Cr92] J. E. Cremona, Algorithms for Modular Elliptic Curves, Cambridge Univ. Press, 1992. The programs mrank, mwrank, findinf may be downloaded from John Cremona's ftp site euclid.ex.ac.uk/pub/cremona.
  • [D95] S. David, Minorations de formes linéaires de logarithmes elliptiques, Mém. Soc. Math. France (N.S.) 62 (1995), iv + 143 pp.
  • [GPZ94] J. Gebel, A. Pethő and H. G. Zimmer, Computing integral points on elliptic curves, Acta Arith. 68 (1994), 171-192.
  • [GPZ97] J. Gebel, A. Pethő and H. G. Zimmer, Computing integral points on Mordell's elliptic curves, Collect. Math. 48 (1997), no. 1-2, 115-136.
  • [HS93] L. Habsieger and D. Stanton, More zeros of Krawtchouk polynomials, Graphs Combin. 9 (1993), 163-172.
  • [HP98] L. Hajdu and Á. Pintér, Combinatorial diophantine equations, preprint.
  • [H97] G. Hanrot, Résolution effective d'équations diophantiennes: algorithmes et applications, Thèse, Université Bordeaux 1, 1997.
  • [KL96] I. Krasikov and S. Litsyn, On integral zeros of Krawtchouk polynomials, J. Combin. Theory Ser. A 74 (1996), 71-99.
  • [N28] T. Nagel, Sur les propriétés des cubiques planes du premier genre, Acta Math. 52 (1928), 93-126.
  • [Sch92] W. M. Schmidt, Integer points on curves of genus 1, Compositio Math. 81 (1992), 33-59.
  • [Sie29] C. L. Siegel, Über einige Anwendungen diophantischer Approximationen, Abh. Preuss. Akad. Wiss. 1929, 1-41.
  • [Sik95] S. Siksek, Infinite descent on elliptic curves, Rocky Mountain J. Math. 25 (1995), 1501-1538.
  • [Sil90] J. H. Silverman, The difference between the Weil height and the canonical height on elliptic curves, Math. Comp. 55 (1990), 723-743.
  • [Sm94] N. P. Smart, S-integral points on elliptic curves, Math. Proc. Cambridge Philos. Soc. 116 (1994), 391-399.
  • [St95] R. J. Stroeker, On the sum of consecutive cubes being a perfect square, Compositio Math. 97 (1995), 295-307.
  • [ST94] R. J. Stroeker and N. Tzanakis, Solving elliptic diophantine equations by estimating linear forms in elliptic logarithms, Acta Arith. 67 (1994), 177-196.
  • [ST97] R. J. Stroeker and N. Tzanakis, On the elliptic logarithm method for elliptic diophantine equations: Reflections and an improvement, Experiment. Math., to appear.
  • [SdW97] R. J. Stroeker and B. M. M. de Weger, Elliptic binomial diophantine equations, Math. Comp., to appear.
  • [SdW98] R. J. Stroeker and B. M. M. de Weger, On integral zeroes of binary Krawtchouk polynomials, Proceedings NMC 1998 (Dutch Math. Congress, Twente Un.), to appear.
  • [Tz96] N. Tzanakis, Solving elliptic diophantine equations by estimating linear forms in elliptic logarithms. The case of quartic equations, Acta Arith. 75 (1996), 165-190.
  • [TdW89] N. Tzanakis and B. M. M. de Weger, On the practical solution of the Thue equation, J. Number Theory 31 (1989), 99-132.
  • [dW89] B. M. M. de Weger, Algorithms for Diophantine equations, CWI Tract 65, Stichting Mathematisch Centrum, Amsterdam, 1989.
  • [Z87] D. Zagier, Large integral points on elliptic curves, Math. Comp.48 (1987), 425-436.
Typ dokumentu
Bibliografia
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