Trinomials defining quintic number fields

被引：1

作者：

Patsolic, Jesse ^{[1
]}

Rouse, Jeremy ^{[2
]}

机构：

[1] Johns Hopkins Univ, Ctr Imaging Sci, Baltimore, MD 21218 USA

[2] Wake Forest Univ, Dept Math & Stat, Winston Salem, NC 27109 USA

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2017年 / 13卷 / 07期

关键词：

Trinomials; elliptic curves; number fields; Chabauty's method; ELLIPTIC-CURVES; POLYNOMIALS; POINTS;

D O I：

10.1142/S1793042117501032

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given a quintic number field K/Q, we study the set of irreducible trinomials, polynomials of the form x(5) + ax + b, that have a root in K. We show that there is a genus 4 curve C-K whose rational points are in bijection with such trinomials. This curve C-K maps to an elliptic curve defined over a number field, and using this map, we are able (in some cases) to determine all the rational points on CK using elliptic curve Chabauty.

引用

页码：1881 / 1894

页数：14

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