某些四次曲线上的发生器和积分点

IF 0.5 4区数学 Q3 MATHEMATICS

Glasnik Matematicki Pub Date : 2019-12-11 DOI:10.3336/gm.54.2.04

Y. Fujita, T. Nara

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引用次数: 0

摘要

本文研究了非零整数m的形式为u2±v4 = m的四次曲线上的积分点和生成点。主要结果表明，在莫德尔-魏尔阶不超过2的情况下，曲线上的某些积分点可以推广为椭圆曲线的莫德尔-魏尔群的基。作为推论，我们明确地描述了在秩为1和2的每种情况下，四次曲线上的积分点。

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Generators and integral points on certain quartic curves

In this paper, we study integral points and generators on quartic curves of the forms u2±v4 = m for a nonzero integer m. The main results assert that certain integral points on the curves can be extended to bases for the Mordell-Weil groups of the elliptic curves attached to the quartic curves in the cases where the Mordell-Weil ranks are at most two. As corollaries, we explicitly describe the integral points on the quartic curves in each case where the ranks are one and two.

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来源期刊

Glasnik Matematicki MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Glasnik Matematicki publishes original research papers from all fields of pure and applied mathematics. The journal is published semiannually, in June and in December.