ArticleOriginal scientific text
Title
A quantitative version of Runge's theorem on diophantine equations
Authors 1
Affiliations
- Department of Pure Mathematics, the University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1
Bibliography
- Y. André, G-functions and Geometry, Vieweg, Braunschweig 1989.
- M. Ayad, Sur le théorème de Runge, Acta Arith. 58 (1991), 203-209.
- J. Coates, Construction of rational functions on a curve, Proc. Cambridge Philos. Soc. 68 (1970), 105-123.
- B. M. Dwork and A. J. van der Poorten, The Eisenstein constant, Macquarie Math. reports, report No.90-0062R (1991). (To appear in Duke Math. J.).
- M. Eichler, Introduction to the Theory of Algebraic Numbers and Functions, Academic Press, London 1966.
- G. Eisenstein, Über eine allgemeine Eigenschaft der Reihen-Entwicklungen aller algebraischen Funktionen, Bericht Königl. Preuss. Akad. d. Wiss. zu Berlin (1852), 441-443.
- W. J. Ellison, Variations sur un thème de Carl Runge, Séminaire Delange-Pisot- Poitou 13 (1970-71), 9.01-9.04.
- A. Grytczuk and A. Schinzel, On Runge's theorem about diophantine equations, to appear in Colloq. Math. Soc. J. Bolyai 60, 1992.
- C. Hermite, Cours de M. Hermite rédigé en 1882, 4th ed., Hermann, Paris 1891.
- D. L. Hilliker and E. G. Straus, Determination of bounds for the solutions to those binary diophantine equations that satisfy the hypotheses of Runge's Theorem, Trans. Amer. Math. Soc. 280 (1983), 637-657.
- D. L. Hilliker and E. G. Straus, On Puiseux series whose curves pass through an infinity of algebraic lattice points, Bull. Amer. Math. Soc. (N.S.) 8 (1983), 59-62.
- D. W. Masser, Polynomial bound for Diophantine equations, Amer. Math. Monthly 93 (1980), 486-488.
- L. J. Mordell, Diophantine Equations, Academic Press, London 1969.
- C. Runge, Über ganzzahlige Lösungen von Gleichungen zwischen zwei Veränder- lichen, J. Reine Angew. Math. 100 (1887), 425-435.
- A. Schinzel, An improvement of Runge's Theorem on diophantine equations, Comment. Pontificia Acad. Sci. 2 (1969), 1-9.
- W. M. Schmidt, Eisenstein's theorem on power series expansions of algebraic functions, Acta Arith. 56 (1990), 161-179.
- T. N. Shorey and R. Tijdeman, Exponential Diophantine Equations, Cambridge University Press, Cambridge 1986.
- T. Skolem, Diophantische Gleichungen, J. Springer, Berlin 1938; reprinted by Chelsea, New York 1950.
- V. G. Sprindžuk, Classical Diophantine Equations in Two Unknowns, Nauka, Moskva 1982 (in Russian).
- J. Turk, On the difference between perfect powers, Acta Arith. 45 (1986), 289-307.
- R. J. Walker, Algebraic Curves, Princeton University Press, Princeton, New Jersey, 1950.