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1996 | 75 | 2 | 165-190
Tytuł artykułu

Solving elliptic diophantine equations by estimating linear forms in elliptic logarithms. The case of quartic equations

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Czasopismo
Rocznik
Tom
75
Numer
2
Strony
165-190
Opis fizyczny
Daty
wydano
1996
otrzymano
1995-07-10
poprawiono
1995-09-17
Twórcy
autor
  • Department of Mathematics, University of Crete, P.O. Box 470, 714 09 Iraklion, Greece
Bibliografia
  • [B] R. T. Bumby, The diophantine equation 3x⁴-2y²=1, Math. Scand. 21 (1967), 144-148.
  • [Cn] I. Connell, Addendum to a paper of Harada and Lang, J. Algebra 145 (1992), 463-467.
  • [Cx] D. A. Cox, The arithmetic-geometric mean of Gauss, Enseign. Math. 30 (1984), 275-330.
  • [Da] S. David, Minorations de formes linéaires de logarithmes elliptiques, Mém. 62 Soc. Math. France (Suppl. to Bull. Soc. Math. France 123 (3) (1995)), to appear.
  • [Di] L. E. Dickson, History of the Theory of Numbers, Vol. II, Chelsea, New York, 1971.
  • [GPZ] J. Gebel, A. Pethő and H. G. Zimmer, Computing integral points on elliptic curves, Acta Arith. 68 (1994), 171-192.
  • [G] R. K. Guy, Reviews in Number Theory 1973-83, Vol. 2A, Amer. Math. Soc., Providence, R.I., 1984.
  • [HK] N. Hirata-Kohno, Formes linéaires de logarithmes de points algébriques sur les groupes algébriques, Invent. Math. 104 (1991), 401-433.
  • [LLL] A. K. Lenstra, H. W. Lenstra and L. Lovász, Factoring polynomials with rational coefficients, Math. Ann. 261 (1982), 515-534.
  • [LV] W. J. LeVeque, Reviews in Number Theory 1940-72, Vol. 2, Amer. Math. Soc., Providence, R.I., 1974.
  • [L1] W. Ljunggren, Einige Sätze über unbestimmte Gleichungen von der Form Ax⁴ +Bx² +C = Dy², Vid.-Akad. Skrifter I (9) (1942), 53 pp.
  • [L2] W. Ljunggren, Zur Theorie der Gleichung X² +1 = DY⁴, Avh. Norske Vid. Akad. Oslo I (5) (1942), 27 pp.
  • [L3] W. Ljunggren, Proof of a theorem of de Jonquières, Norsk Mat. Tidsskrift 26 (1944), 3-8 (in Norwegian).
  • [S1] J. H. Silverman, Computing heights on elliptic curves, Math. Comp. 51 (1988), 339-358.
  • [S2] J. H. Silverman, The difference between the Weil height and the canonical height on elliptic curves, Math. Comp. 55 (1990), 723-743.
  • [StT] R. Steiner and N. Tzanakis, Simplifying the solution of Ljunggren's equation X² +1 = 2Y⁴, J. Number Theory 37 (1991), 123-132.
  • [Str] R. J. Stroeker, On the sum of consecutive cubes being a perfect square, Compositio Math. 97 (1995), 295-307.
  • [ST] R. J. Stroeker and N. Tzanakis, Solving elliptic diophantine equations by estimating linear forms in elliptic logarithms, Acta Arith. 67 (1994), 177-196.
  • [SW] R. J. Stroeker and B. M. M. de Weger, On a quartic Diophantine equation, Proc. Edinburgh Math. Soc., to appear.
  • [T1] J. Top, Fermat's 'primitive solutions' and some arithmetic of elliptic curves, Indag. Math. 4 (1993), 211-222.
  • [T2] J. Top, Examples of elliptic quartics with many integral points, private communication, September 1994.
  • [dW] B. M. M. de Weger, Algorithms for diophantine equations, CWI Tract 65, Centre for Mathematics and Computer Science, Amsterdam, 1989.
  • [Z] D. Zagier, Large integral points on elliptic curves, Math. Comp. 48 (1987), 425-436
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-aav75i2p165bwm
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