@article{bwmeta1.element.bwnjournal-article-aav86i1p51bwm,
author = {Dimitrios Poulakis},
title = {Bounds for the minimal solution of genus zero diophantine equations},
journal = {Acta Arithmetica},
volume = {84},
year = {1998},
pages = {51-90},
zbl = {0934.11035},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav86i1p51bwm}
}
Dimitrios Poulakis. Bounds for the minimal solution of genus zero diophantine equations. Acta Arithmetica, Tome 84 (1998) pp. 51-90. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav86i1p51bwm/
[000] [1] G. A. Bliss, Algebraic Functions, Dover, New York, 1966. | Zbl 0141.05002
[001] [2] E. Brieskorn and H. Knörrer, Plane Algebraic Curves, Birkhäuser, 1986.
[002] [3] M. Eichler, Introduction to the Theory of Algebraic Numbers and Functions, Academic Press, New York, 1966.
[003] [4] W. Fulton, Algebraic Curves, Benjamin, New York, 1969. | Zbl 0181.23901
[004] [5] R. Hartshorne, Algebraic Geometry, Springer, 1977.
[005] [6] D. Hilbert und A. Hurwitz, Über die diophantischen Gleichungen von Geschlecht Null, Acta Math. 14 (1890), 217-224.
[006] [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. | Zbl 0569.12009
[007] [8] L. Holzer, Minimal solutions of diophantine equations, Canad. J. Math. 2 (1950), 238-244.
[008] [9] S. Lang, Introduction to Algebraic and Abelian Functions, Springer, 1982. | Zbl 0513.14024
[009] [10] S. Lang, Fundamentals of Diophantine Geometry, Springer, 1983. | Zbl 0528.14013
[010] [11] M. Mignotte, An inequality on the greatest roots of a polynomial, Elem. Math. 46 (1991), 85-86. | Zbl 0745.12001
[011] [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.
[012] [13] H. Poincaré, Sur les propriétés arithmétiques des courbes algébriques, J. Math. Pures Appl. 71 (1901), 161-233. | Zbl 32.0564.06
[013] [14] D. Poulakis, Integer points on algebraic curves with exceptional units, J. Austral. Math. Soc. 63 (1997), 145-164. | Zbl 0893.11010
[014] [15] D. Poulakis, Polynomial bounds for the solutions of a class of Diophantine equations, J. Number Theory 66 (1997), 271-281.
[015] [16] S. Raghavan, Bounds for minimal solutions of diophantine equations, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II 1975, no. 9, 109-114. | Zbl 0317.10025
[016] [17] W. M. Schmidt, Eisenstein's theorem on power series expansions of algebraic functions, Acta Arith. 56 (1990), 161-179. | Zbl 0659.12003
[017] [18] W. M. Schmidt, Construction and estimation of bases in function fields, J. Number Theory 39 (1991), 181-224. | Zbl 0764.11046
[018] [19] J. G. Semple and L. Roth, Algebraic Geometry, Oxford University Press, 1949.
[019] [20] C. L. Siegel, Normen algebraischer Zahlen, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II 1973, no. 11, 197-215. | Zbl 0294.10010
[020] [21] J. H. Silverman, The Arithmetic of Elliptic Curves, Springer, 1986. | Zbl 0585.14026
[021] [22] R. Walker, Algebraic Curves, Springer, 1978.