Bounds for the minimal solution of genus zero diophantine equations

Dimitrios Poulakis

Acta Arithmetica (1998)

  • Volume: 86, Issue: 1, page 51-90
  • ISSN: 0065-1036

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Dimitrios Poulakis. "Bounds for the minimal solution of genus zero diophantine equations." Acta Arithmetica 86.1 (1998): 51-90. <http://eudml.org/doc/207181>.

@article{DimitriosPoulakis1998,
author = {Dimitrios Poulakis},
journal = {Acta Arithmetica},
keywords = {bounds for minimal solution; genus zero curve},
language = {eng},
number = {1},
pages = {51-90},
title = {Bounds for the minimal solution of genus zero diophantine equations},
url = {http://eudml.org/doc/207181},
volume = {86},
year = {1998},
}

TY - JOUR
AU - Dimitrios Poulakis
TI - Bounds for the minimal solution of genus zero diophantine equations
JO - Acta Arithmetica
PY - 1998
VL - 86
IS - 1
SP - 51
EP - 90
LA - eng
KW - bounds for minimal solution; genus zero curve
UR - http://eudml.org/doc/207181
ER -

References

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  1. [1] G. A. Bliss, Algebraic Functions, Dover, New York, 1966. Zbl0141.05002
  2. [2] E. Brieskorn and H. Knörrer, Plane Algebraic Curves, Birkhäuser, 1986. 
  3. [3] M. Eichler, Introduction to the Theory of Algebraic Numbers and Functions, Academic Press, New York, 1966. 
  4. [4] W. Fulton, Algebraic Curves, Benjamin, New York, 1969. Zbl0181.23901
  5. [5] R. Hartshorne, Algebraic Geometry, Springer, 1977. 
  6. [6] D. Hilbert und A. Hurwitz, Über die diophantischen Gleichungen von Geschlecht Null, Acta Math. 14 (1890), 217-224. 
  7. [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. Zbl0569.12009
  8. [8] L. Holzer, Minimal solutions of diophantine equations, Canad. J. Math. 2 (1950), 238-244. 
  9. [9] S. Lang, Introduction to Algebraic and Abelian Functions, Springer, 1982. Zbl0513.14024
  10. [10] S. Lang, Fundamentals of Diophantine Geometry, Springer, 1983. Zbl0528.14013
  11. [11] M. Mignotte, An inequality on the greatest roots of a polynomial, Elem. Math. 46 (1991), 85-86. Zbl0745.12001
  12. [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. [13] H. Poincaré, Sur les propriétés arithmétiques des courbes algébriques, J. Math. Pures Appl. 71 (1901), 161-233. Zbl32.0564.06
  14. [14] D. Poulakis, Integer points on algebraic curves with exceptional units, J. Austral. Math. Soc. 63 (1997), 145-164. Zbl0893.11010
  15. [15] D. Poulakis, Polynomial bounds for the solutions of a class of Diophantine equations, J. Number Theory 66 (1997), 271-281. 
  16. [16] S. Raghavan, Bounds for minimal solutions of diophantine equations, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II 1975, no. 9, 109-114. Zbl0317.10025
  17. [17] W. M. Schmidt, Eisenstein's theorem on power series expansions of algebraic functions, Acta Arith. 56 (1990), 161-179. Zbl0659.12003
  18. [18] W. M. Schmidt, Construction and estimation of bases in function fields, J. Number Theory 39 (1991), 181-224. Zbl0764.11046
  19. [19] J. G. Semple and L. Roth, Algebraic Geometry, Oxford University Press, 1949. 
  20. [20] C. L. Siegel, Normen algebraischer Zahlen, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II 1973, no. 11, 197-215. Zbl0294.10010
  21. [21] J. H. Silverman, The Arithmetic of Elliptic Curves, Springer, 1986. Zbl0585.14026
  22. [22] R. Walker, Algebraic Curves, Springer, 1978. 

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