INTEGER POINTS ON ELLIPTIC CURVES

被引：3

作者：

Vaughan, R. . C. . ^{[1
]}

机构：

[1] Penn State Univ, Dept Math, University Pk, PA 16802 USA

来源：

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2014年 / 44卷 / 04期

关键词：

D O I：

10.1216/RMJ-2014-44-4-1377

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that the number of integer points on an elliptic curve y(2) = f(x) with X-0 < x <= X-0 + X is << X-1/2 where the implicit constant depends at most on the degree of f(x). This improves on various bounds of Cohen [4], Bombieri and Pila [1] and of Pila [9], and others. In particular it follows that the number of positive integral solutions to x(3) + y(2) = n is << n(1/6).

引用

页码：1377 / 1382

页数：6

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