Plane curves in boxes and equal sums of two powers
Plane curves in boxes and equal sums of two powers
复制标题
盒子中的平面曲线和二次幂的等和
DOI：
10.1007/s00209-004-0719-z
复制
发表时间：
2005
影响因子：
0.8
通讯作者：
D. R. Heath
中科院分区：
文献类型：
--
作者：
T. Browning;D. R. Heath
设F ∈ Z[x1，x2，x3]是一个d次绝对不可约形式，在P中生成一条平面曲线，本文的主要目的是分析这类曲线上包含在不等边盒中的有理点的密度.我们将在下面看到如何利用这些考虑来获得两个幂和相等的新的贫量结果。设P =（P1，P2，P3），其中固定的真实的数为1 ≤ P1 ≤ P2 ≤ P3。然后我们定义
Let F ∈ Z[x1, x2, x3] be an absolutely irreducible form of degree d, producing a plane curve in P. The central aim of this paper is to analyze the density of rational points on such curves, which are contained in boxes with unequal sides. We shall see below how such considerations may be used to obtain new paucity results for equal sums of two powers. Suppose that P = (P1, P2, P3) for fixed real numbers 1 ≤ P1 ≤ P2 ≤ P3, say. Then we define