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Original Articles

Calculating “Small” Solutions of Relative Thue Equations

REFERENCES

  • [Baker 90] A. Baker. Transcendental Number Theory. Cambridge Univ. Press, 1990.
  • [Fincke and Pohst 85] U. Fincke and M. Pohst. “Improved Methods for Calculating Vectors of Short Length in a Lattice, Including a Complexity Analysis.” Math. Comput. 44 (1985), 463–471.
  • [Gaál 96a] I. Gaál. “Application of Thue Equations to Computing Power Integral Bases in Algebraic Number Fields.” Proc. Conf. ANTS II, Talence, France, 1996, Lecture Notes in Computer Science 1122, pp. 151–155. Springer, 1996.
  • [Gaál 96b] I. Gaál. “Computing All Power Integral Bases in Orders of Totally Real Cyclic Sextic Number Fields.” Math. Comput. 65 (1996), 801–822.
  • [Gaál 00] I. Gaál. “Solving Index Form Equations in Fields of Degree Nine with Cubic Subfields.” J. Symbolic Comput. 30 (2000), 181–193.
  • [Gaál 02] I. Gaál. Diophantine Equations and Power Integral Bases. Birkhäuser, 2002.
  • [Gaál and Pohst 96] I. Gaál and M. Pohst. “On the Resolution of Index Form Equations in Sextic Fields with an Imaginary Quadratic Subfield.” J. Symbolic Comput. 22 (1996), 425–434.
  • [Gaál and Pohst 00] I. Gaál and M. Pohst. “On the Resolution of Index Form Equations in Relative Quartic Extensions.” J. Number Theory 85 (2000), 201–219.
  • [Gaál and Pohst 02] I. Gaál and M. Pohst. “On the Resolution of Relative Thue Equations.” Math. Comput. 71 (2002), 429–440.
  • [Gaál and Remete 14] I. Gaál and L. Remete. “Binomial Thue Equations and Power Integral Bases in Pure Quartic Fields.” JP Journal of Algebra, Number Theory and Applications 32 (2014), 49–61.
  • [Gaál and Szabó 10] I. Gaál and T. Szabó. “A Note on the Minimal Indices of Pure Cubic Fields.” JP Journal of Algebra, Number Theory and Applications 19 (2010), 129–139.
  • [Gaál and Szabó 12] I. Gaál and T. Szabó. “Power Integral Bases in Parametric Families of Biquadratic Fields.” JP Journal of Algebra, Number Theory and Applications 21 (2012), 105–114.
  • [Gaál and Szabó 13] I. Gaál and T. Szabó. “Relative Power Integral Bases in Infinite Families of Quartic Extensions of Quadratic Fields.” JP Journal of Algebra, Number Theory and Applications 29 (2013), 31–43.
  • [Gaál et al. 96] I. Gaál, A. Pethő, and M. 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 57 (1996), 90–104.
  • [Lenstra et al. 82] A. K. Lenstra, H. W. Lenstra Jr, and L. Lovász. “Factoring Polynomials with Rational Coefficients.” Math. Ann. 261 (1982), 515–534.
  • [Pethő 87] A. Pethő. “On the Resolution of Thue Inequalities.” J. Symbolic Comput. 4 (1987), 103–109.
  • [Pohst 93] M. Pohst. “Computational Algebraic Number Theory,” DMV Seminar 21. Birkhäuser, 1993.
  • [Pohst and Zassenhaus 89] M. Pohst and H. Zassenhaus. “Algorithmic Algebraic Number Theory.” Cambridge University Press, 1989.
  • [Thue 09] A. Thue. “Über Annäherungswerte algebraischer Zahlen.” J. Reine Angew. Math. 135 (1909), 284–305.
  • [Voight 08] J. Voight. “Enumeration of Totally Real Number Fields of Bounded Root Discriminant.” In Algorithmic Number Theory, Proc. ANTS-VIII Banff, Canada, May 17–22, 2008, Lecture Notes in Computer Science 5011, pp. 268–281. Berlin: Springer, 2008.

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