Construction of rational functions on a curve
Construction of rational functions on a curve
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曲线上有理函数的构造
DOI：
10.1017/s0305004100001110
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发表时间：
1970
影响因子：
0.8
通讯作者：
J. Coates
中科院分区：
文献类型：
--
作者：
J. Coates
1. 介绍。在研究双变量丢芬图方程时，经常需要考虑具有指定零点和极点的曲线上的有理函数。虽然众所周知，这种函数原则上总是可以有效地构造，但似乎没有给出详细的证明。本文的目的是给出这种构造的完整证明。我们的方法，我们的结果的陈述，是由我们所想到的丢番图方程的应用所激发的。特别是，我们的结果将在随后的论文(1)中发挥重要作用，其中将为任何属1的曲线上的整数点建立显式界限。
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.