ArticleOriginal scientific text

Title

Bounds for the minimal solution of genus zero diophantine equations

Authors 1

Affiliations

  1. Department of Mathematics, Aristotle University of Thessaloniki, 54006 Thessaloniki, Greece

Bibliography

  1. G. A. Bliss, Algebraic Functions, Dover, New York, 1966.
  2. E. Brieskorn and H. Knörrer, Plane Algebraic Curves, Birkhäuser, 1986.
  3. M. Eichler, Introduction to the Theory of Algebraic Numbers and Functions, Academic Press, New York, 1966.
  4. W. Fulton, Algebraic Curves, Benjamin, New York, 1969.
  5. R. Hartshorne, Algebraic Geometry, Springer, 1977.
  6. D. Hilbert und A. Hurwitz, Über die diophantischen Gleichungen von Geschlecht Null, Acta Math. 14 (1890), 217-224.
  7. D. L. Hilliker, An algorithm for computing the values of the ramification index in the Puiseux series expansions of an algebraic function, Pacific J. Math. 118 (1985), 427-435.
  8. L. Holzer, Minimal solutions of diophantine equations, Canad. J. Math. 2 (1950), 238-244.
  9. S. Lang, Introduction to Algebraic and Abelian Functions, Springer, 1982.
  10. S. Lang, Fundamentals of Diophantine Geometry, Springer, 1983.
  11. M. Mignotte, An inequality on the greatest roots of a polynomial, Elem. Math. 46 (1991), 85-86.
  12. L. J. Mordell, On the magnitude of the integer solutions of the equation ax²+by²+cz²=0, J. Number Theory 1 (1969), 1-3.
  13. H. Poincaré, Sur les propriétés arithmétiques des courbes algébriques, J. Math. Pures Appl. 71 (1901), 161-233.
  14. D. Poulakis, Integer points on algebraic curves with exceptional units, J. Austral. Math. Soc. 63 (1997), 145-164.
  15. D. Poulakis, Polynomial bounds for the solutions of a class of Diophantine equations, J. Number Theory 66 (1997), 271-281.
  16. S. Raghavan, Bounds for minimal solutions of diophantine equations, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II 1975, no. 9, 109-114.
  17. W. M. Schmidt, Eisenstein's theorem on power series expansions of algebraic functions, Acta Arith. 56 (1990), 161-179.
  18. W. M. Schmidt, Construction and estimation of bases in function fields, J. Number Theory 39 (1991), 181-224.
  19. J. G. Semple and L. Roth, Algebraic Geometry, Oxford University Press, 1949.
  20. C. L. Siegel, Normen algebraischer Zahlen, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II 1973, no. 11, 197-215.
  21. J. H. Silverman, The Arithmetic of Elliptic Curves, Springer, 1986.
  22. R. Walker, Algebraic Curves, Springer, 1978.
Pages:
51-90
Main language of publication
English
Received
1997-10-31
Accepted
1998-03-03
Published
1998
Exact and natural sciences