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On the number of solutions of linear equations in units of an algebraic number field

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Commentarii Mathematici Helvetici

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References

  1. Baker, A.,Contributions to the theory of Diophantine equations, Philos. Trans. Roy. Soc. London, Ser. A,263 (1968), 173–208.

    Article  MathSciNet  MATH  Google Scholar 

  2. —,A sharpening of the bounds for linear forms in logarithms II, Acta Arith.,25 (1973), 33–36.

    MathSciNet  MATH  Google Scholar 

  3. Baker, A., Transcendental number theory, Cambridge, 1975.

  4. Choodnovsky, G. V.,The Gelfond-Baker method in problems of diophantine approximation, Colloquia Math. Soc. János Bolyai,13. Topics in number theory, Debrecen, 1974; pp. 19–30 (1976).

  5. Dobrowolski E.,On the maximal modulus of conjugates of an algebraic integer, Bull. Acad. Polon. Sci.,26 (1978), 291–92.

    MathSciNet  MATH  Google Scholar 

  6. Györy, K.,Sur l'irréductibilité d'une classe des polynômes II, Publ. Math. Debrecen,19 (1972) 293–326.

    MathSciNet  MATH  Google Scholar 

  7. —,Sur une classe des corps de nombres algébriques et ses applications, Publ. Math. Debrecen,22 (1975), 151–175.

    MathSciNet  MATH  Google Scholar 

  8. —,On polynomials with integer coefficients and given discriminant V, p-adic generalizations, Acta Math. Acad. Sci. Hungar.,32 (1978), 175–190.

    Article  MathSciNet  MATH  Google Scholar 

  9. Györy, K.,On the solutions of linear diophantine equations in algrebraic integers of bounded norm, Ann. Univ. Budapest Eötvös, Sect. Math., to appear.

  10. Györy, K.,On the reducibility of a class of polynomials III, 26 (1978), 291–92.

  11. Lang, S.,Diophantine geometry, New York and London, 1962.

  12. Lewis, D. J. andMahler, K.,On the representation of integers by binary forms, Acta Arith.,6 (1961), 333–363.

    MathSciNet  MATH  Google Scholar 

  13. Mahler, K.,On algebraic relations between two units of an algebraic field, Algebre et Théorie des Nombres, Colloques Internationaux du Centre National de la Recherche Scientifique, No. 24, pp. 47–55, CNRS, Paris, 1950.

    MATH  Google Scholar 

  14. Mordell, L. J.,Diophantine equations, Academic Press, London and New York, 1969.

    MATH  Google Scholar 

  15. Nagell, T.,Sur une propriété des unités d'un corps algébrique, Arkiv för Mat.,5 (1964), 343–356.

    Article  MathSciNet  MATH  Google Scholar 

  16. —,Quelques problèmes relatifs auz unités algébriques, Arkiv för Mat.,8 (1969), 115–127.

    Article  MathSciNet  MATH  Google Scholar 

  17. —,Sur un type particulier d'unités algébriques, Arkiv för Mat.,8 (1969), 163–184.

    Article  MathSciNet  MATH  Google Scholar 

  18. Newman, M.,Units in arithmetic progression in an algebraic number field, Proc. Amer. Math. Soc.,43 (1974), 266–268.

    Article  MathSciNet  MATH  Google Scholar 

  19. Parry, C. J.,The P-adic generalisation of the Thue-Siegel theorem, Acta Math.,83 (1950), 1–100.

    Article  MathSciNet  MATH  Google Scholar 

  20. van der Poorten, A. J., Linear forms in logarithms in the p-adic case,Transcendence Theory: Advances and Applications, pp. 29–57. Academic Press, London and New York, 1977.

    MATH  Google Scholar 

  21. — andLoxton, J. H.,Multiplicative relations in number fields, Bull. Austral. Math. Soc.,16, (1977), 83–98. Corregindum and addendum, ibid.,17 (1977), 151–156.

    Article  MathSciNet  MATH  Google Scholar 

  22. Siegel, C. L.,Approximation algebraischen,Zahlen, Math. Z.,10 (1921), 173–213.

    Article  MATH  Google Scholar 

  23. —,The integer solutions of the equation y 2=ax n+bx n−1+...+k, J. London Math. Soc.1 (1926), 66–68.

    MathSciNet  Google Scholar 

  24. —,Abschätzung von Einheiten, Nachr. Akad. Wiss. Göttingen, Math.-Phys. Kl.II (1969), 71–86.

    MATH  Google Scholar 

  25. Skolem, Th.,Diophantische Gleichungen, Springer Verlag, Berlin, 1938.

    MATH  Google Scholar 

  26. Sprindžuk, V. G.,Algebraic number fields with large class number (in Russian), Izv. Akad. Nauk SSSR, Ser. Mat.,38 (1974), 971–982.

    MathSciNet  MATH  Google Scholar 

  27. —,Hyperelliptic diophantine equation and class numbers (in Russian), Acta Arith.,30 (1976), 95–108.

    MathSciNet  MATH  Google Scholar 

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Györy, K. On the number of solutions of linear equations in units of an algebraic number field. Commentarii Mathematici Helvetici 54, 583–600 (1979). https://doi.org/10.1007/BF02566294

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