On uniform bounds for rational points on nonrational curves
On uniform bounds for rational points on nonrational curves
复制标题
关于非有理曲线上有理点的统一界限
DOI：
10.1155/imrn.2005.2163
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发表时间：
2005
影响因子：
1
通讯作者：
Akshay Venkatesh
中科院分区：
文献类型：
--
作者：
J. Ellenberg;Akshay Venkatesh
证明了d次非有理平面曲线上高度≤ H的有理点的个数为Od（H2/d-δ），其中δ > 0只与d有关.隐式常数仅取决于d。这改进了Heath-Brown的一个结果，他证明了O（H2/d+）界。我们还表明，在d = 3的情况下，可以取δ = 1/450。
We show that the number of rational points of height ≤ H on a non-rational plane curve of degree d is Od(H 2/d−δ), for some δ > 0 depending only on d. The implicit constant depends only on d. This improves a result of Heath-Brown, who proved the bound O (H2/d+ ). We also show that one can take δ = 1/450 in the case d = 3.