Complete solution of a family of quartic Thue equations

  • G. Lettl
  • A. Pethő


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  1. [1]
    A. Baker. Contribution to the theory of Diophantine equations I. On the representation of integers by binary forms.Philos. Trans. Roy. Soc. Londen 263 (1968), 173–191.MATHCrossRefGoogle Scholar
  2. [2]
    I. Gaál. On the resolution of some diophantine equations. In:Computational Number Theory, Colloquim on Computational Number Theory, Debrecen, 1989. Eds.: A. Pethő, M. Pohst, H.C. Williams, H.G. Zimmer. De Gruyter 1991, 261–280.Google Scholar
  3. [3]
    I. Gaál, A. Pethő andM. Pohst. On the resolution of a family of index form equations in quartic number fields.J. Symbolic Comp. 16 (1993), 563–584.MATHCrossRefGoogle Scholar
  4. [4]
    I. Gaál, A. Pethő andM. Pohst. Simultaneous representation of integers by a pair of ternary quadratic forms with an application to index form equations in quartic number fields.J. Number Theory, to appear.Google Scholar
  5. [5]
    M. N. Gras. Table numerique du nombre de classe et des unites des extensions cycliques reelles de degré 4 de ℒ.Publ. Math. Fac. Sci. Besançon (1977–1978), fasc. 2.Google Scholar
  6. [6]
    A. J. Lazarus. On the class number and unit index of simplest quartic fields.Nagoya Math. J. 121 (1991), 1–13.MATHMathSciNetGoogle Scholar
  7. [7]
    K. Mahler. An inequality for the discriminant of a polynomial.Michigan Math. J. 11 (1964), 257–262.MATHCrossRefMathSciNetGoogle Scholar
  8. [8]
    M. Mignotte. Verification of a Conjecture of E. Thomas.J. Number Theory 44 (1993), 172–177.MATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    M. Mignotte, A. Pethő andR. Roth. Complete solutions of quartic Thue and index form equations.Math. Comp., to appear.Google Scholar
  10. [10]
    M. Mignotte andN. Tzanakis. On a family of cubics.J. Number Theory 39 (1991), 41–49.MATHCrossRefMathSciNetGoogle Scholar
  11. [11]
    A. Pethő. Complete solutions to families of quartic Thue equations.Math. Comp. 57 (1991), 777–798.CrossRefMathSciNetGoogle Scholar
  12. [12]
    A. Pethő andR. Schulenberg. Effektives Lösen von Thue Gleichungen.Publ. Math. Debrecen 34 (1987), 189–196.MathSciNetGoogle Scholar
  13. [13]
    M. Pohst andH. Zassenhaus.Algorithmic Algebraic Number Theory. Cambridge Univ. Press 1989.Google Scholar
  14. [14]
    D. Shanks. The simplest cubic fields.Math. Comp. 28 (1974), 1134–1152.Google Scholar
  15. [15]
    E. Thomas. Fundamental units for orders in certain cubic number fields.J. reine angew. Math. 310 (1979), 33–55.MATHMathSciNetGoogle Scholar
  16. [16]
    E. Thomas. Complete solutions to a family of cubic diophantine equations.J. Number Theory 34 (1990), 235–250.MATHCrossRefMathSciNetGoogle Scholar
  17. [17]
    E. Thomas. Solutions to certain families of Thue equations.J. Number Theory 43 (1993), 319–369.MATHCrossRefMathSciNetGoogle Scholar
  18. [18]
    A. Thue. Über Annäherungswerte algebraischer Zahlen.J. reine angew. Math. 135 (1909), 284–305.MATHGoogle Scholar
  19. [19]
    N. Tzanakis andB. M. M. de Weger. On the practical solution of the Thue equation.J. Number Theory 31 (1989), 99–132.MATHCrossRefMathSciNetGoogle Scholar
  20. [20]
    M. Waldschmidt.Linear independence of logarithms of algebraic numbers. IMSc. Report116, The Institute of Math. Sciences. Madras 1992.MATHGoogle Scholar

Copyright information

© Mathematische Seminar 1995

Authors and Affiliations

  • G. Lettl
    • 1
  • A. Pethő
    • 2
  1. 1.Institut für MathematikKarl-Franzens-UniversitätGrazAustralia
  2. 2.Laboratory of InformaticsUniversity of MedicineDebrecenHungary

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