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1999 | 91 | 2 | 147-163
Tytuł artykułu

Effective solution of families of Thue equations containing several parameters

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Czasopismo
Rocznik
Tom
91
Numer
2
Strony
147-163
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-11-13
poprawiono
1999-04-13
Twórcy
  • Institut für Mathematik, Technische Universität Graz, Steyrergasse 30, A-8010 Graz, Austria
  • Institut für Mathematik, Technische Universität Graz, Steyrergasse 30, A-8010 Graz, Austria
Bibliografia
  • [1] A. Baker and G. Wüstholz, Logarithmic forms and group varieties, J. Reine Angew. Math. 442 (1993), 19-62.
  • [2] Yu. Bilu and G. Hanrot, Solving Thue equations of high degree, J. Number Theory 60 (1996), 373-392.
  • [3] Y. Bugeaud and K. Győry, Bounds for the solutions of Thue-Mahler equations and norm form equations, Acta Arith. 74 (1996), 273-292.
  • [4] J. H. Chen and P. M. Voutier, Complete solution of the Diophantine equation $X^2 + 1 = dY^4$ and a related family of quartic Thue equations, J. Number Theory 62 (1997), 71-99.
  • [5] I. Gaál, On the resolution of some Diophantine equations, in: Computational Number Theory, A. Pethő, M. Pohst, H. C. Williams and H. G. Zimmer (eds.), de Gruyter, Berlin, 1991, 261-280.
  • [6] I. Gaál and G. Lettl, A parametric family of quintic Thue equations, Math. Comp., to appear.
  • [7] F. Halter-Koch, G. Lettl, A. Pethő and R. F. Tichy, Thue equations associated with Ankeny-Brauer-Chowla number fields, J. London Math. Soc., to appear.
  • [8] C. Heuberger, On families of parametrized Thue equations, J. Number Theory 76 (1999), 45-61.
  • [9] C. Heuberger, On a family of quintic Thue equations, J. Symbolic Comput. 26 (1998), 173-185.
  • [10] C. Heuberger, A. Pethő and R. F. Tichy, Complete solution of parametrized Thue equations, Acta Math. Inform. Univ. Ostraviensis 6 (1998), 93-113.
  • [11] S. Lang, Elliptic Curves: Diophantine Analysis, Grundlehren Math. Wiss. 23, Springer, Berlin, 1978.
  • [12] E. Lee, Studies on Diophantine equations, Ph.D. thesis, Cambridge Univ., 1992.
  • [13] G. Lettl and A. Pethő, Complete solution of a family of quartic Thue equations, Abh. Math. Sem. Univ. Hamburg 65 (1995), 365-383.
  • [14] G. Lettl, A. Pethő and P. Voutier, Simple families of Thue inequalities, Trans. Amer. Math. Soc. 351 (1999), 1871-1894.
  • [15] G. Lettl, A. Pethő and P. Voutier, On the arithmetic of simplest sextic fields and related Thue equations, in: Number Theory, Diophantine, Computational and Algebraic Aspects (Eger, 1996), K. Győry, A. Pethő and V. T. Sós (eds.), de Gruyter, Berlin, 1998, 331-348.
  • [16] M. Mignotte, Verification of a conjecture of E. Thomas, J. Number Theory 44 (1993), 172-177.
  • [17] M. Mignotte, A. Pethő and F. Lemmermeyer, On the family of Thue equations $x^3 - (n-1)x^2y - (n+2)xy^2 - y^3 = k$, Acta Arith. 76 (1996), 245-269.
  • [18] M. Mignotte, A. Pethő and R. Roth, Complete solutions of quartic Thue and index form equations, Math. Comp. 65 (1996), 341-354.
  • [19] M. Mignotte and N. Tzanakis, On a family of cubics, J. Number Theory 39 (1991), 41-49.
  • [20] A. Pethő, Complete solutions to families of quartic Thue equations, Math. Comp. 57 (1991), 777-798.
  • [21] A. Pethő and R. F. Tichy, On two-parametric quartic families of Diophantine problems, J. Symbolic Comput. 26 (1998), 151-171.
  • [22] M. Pohst, Regulatorabschätzungen für total reelle algebraische Zahlkörper, J. Number Theory 9 (1977), 459-492.
  • [23] M. Pohst and H. Zassenhaus, Algorithmic Algebraic Number Theory, Cambridge Univ. Press, Cambridge, 1989.
  • [24] I. Schur, Aufgabe 226, Arch. Math. Physik 13 (1908), 367.
  • [25] E. Thomas, Complete solutions to a family of cubic Diophantine equations, J. Number Theory 34 (1990), 235-250.
  • [26] E. Thomas, Solutions to certain families of Thue equations, ibid. 43 (1993), 319-369.
  • [27] A. Thue, Über Annäherungswerte algebraischer Zahlen, J. Reine Angew. Math. 135 (1909), 284-305.
  • [28] I. Wakabayashi, On a family of quartic Thue inequalities I, J. Number Theory 66 (1997), 70-84.
  • [29] M. Waldschmidt, Minoration de combinaisons linéaires de logarithmes de nombres algébriques, Canad. J. Math. 45 (1993), 176-224.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-aav91i2p147bwm
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