不同椭圆曲线模型上的有理序列

IF 0.5 4区数学 Q3 MATHEMATICS

Glasnik Matematicki Pub Date : 2019-03-17 DOI:10.3336/gm.54.1.04

Gamze Savacs cCEL.IK, M. Sadek, G. Soydan

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引用次数: 1

摘要

给定数域$k$中元素的集合$S$，讨论了$k$上具有有理点的平面代数曲线的存在性，这些有理点的$x$坐标正是$S$的元素。如果$S$的$|S|$的大小为$4,5$或$6$，我们展示了无限的(扭曲的)Edwards曲线和(一般的)Huff曲线族，其中$S$的元素被实现为这些曲线上有理点的$x$坐标。这推广了先前关于某些代数曲线上某些类型级数的工作。

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Rational sequences on different models of elliptic curves

Given a set $S$ of elements in a number field $k$, we discuss the existence of planar algebraic curves over $k$ which possess rational points whose $x$-coordinates are exactly the elements of $S$. If the size $|S|$ of $S$ is either $4,5$, or $6$, we exhibit infinite families of (twisted) Edwards curves and (general) Huff curves for which the elements of $S$ are realized as the $x$-coordinates of rational points on these curves. This generalizes earlier work on progressions of certain types on some algebraic curves.

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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.