Construction of rational functions on a curve
- 1 July 1970
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 68 (1) , 105-123
- https://doi.org/10.1017/s0305004100001110
Abstract
1. Introduction. In the study of diophantine equations in two variables, it is often necessary to consider rational functions on a curve with prescribed zeros and poles. Although it is well known that such functions can, in principle, always be effectively constructed, the detailed proof does not appear to have been given. The purpose of the present paper is to give the complete proof of such a construction. Our method, and the statement of our results, are motivated by the applications to diophantine equations which we have in mind. In particular, our results will play an important role in a subsequent paper (1), in which explicit bounds will be established for the integer points on any curve of genus 1.This publication has 1 reference indexed in Scilit:
- Integer points on curves of genus 1Mathematical Proceedings of the Cambridge Philosophical Society, 1970