Thue's equation over function fields
- 1 June 1978
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of the Australian Mathematical Society
- Vol. 25 (4) , 385-422
- https://doi.org/10.1017/s1446788700021406
Abstract
Suppose we are given a “Thue equation” f(x, y) = 1, where f is a binary form with coefficients in a function field K of characteristic zero. A typical result is that if f is of degree at least 5 and has no multiple factors, then every solution x = (x, y) of the equation with components in K has H(x)≤90H(f) + 250g. Here g is the genus of K and H(x), H(f) are suitably defined heights. No assumption is made that x be “integral” in some sense. As an application, bounds are derived for “integral” solutions of hyperelliptic equations over K.Keywords
This publication has 10 references indexed in Scilit:
- On Osgood's effective thue theorem for algebraic functionsCommunications on Pure and Applied Mathematics, 1976
- Effective bounds on the “diophantine approximation” of algebraic functions over fields of arbitrary characteristic and applications to differential equationsIndagationes Mathematicae, 1975
- An effective lower bound on the “Diophantine approximation” of algebraic functions by rational functionsMathematika, 1973
- Bounds for the solutions of the hyperelliptic equationMathematical Proceedings of the Cambridge Philosophical Society, 1969
- Algebraic functions and an analogue of the geometry of numbers: The Riemann-Roch TheoremArchiv der Mathematik, 1967
- Mordells Vermutung über rationale Punkte auf algebraischen Kurven und FunktionenkörperPublications mathématiques de l'IHÉS, 1965
- Einführung in die Theorie der Algebraischen Zahlen und FunktionenPublished by Springer Nature ,1963
- RATIONAL APPROXIMATIONS TO ALGEBRAIC FUNCTIONSHokkaido Mathematical Journal, 1961
- Über die rationalen Punkte auf Kurven vom Geschlecht Eins.Journal für die reine und angewandte Mathematik (Crelles Journal), 1934
- Zur Approximation algebraischer Zahlen. IMathematische Annalen, 1933