ALGEBRAIC POINTS OF GIVEN DEGREE ON THE AFFINE CURVE C : y2 = x5

被引：0

作者：

Sow, E. L. Hadji ^{[1
]}

Fall, Moussa ^{[1
]}

Sall, Oumar ^{[1
]}

机构：

[1] Assane SECK Univ Ziguinchor, UFR Sci & Technol Math & Applicat Lab, Ziguinchor, Senegal

来源：

JP JOURNAL OF ALGEBRA NUMBER THEORY AND APPLICATIONS | 2023年 / 60卷 / 02期

关键词：

planes curves; degree of algebraic points; rational points; algebraic extensions; Jacobian;

D O I：

10.17654/0972555523004

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this work, we determine the set of algebraic points of a given degree over Q on the curve of affine equation y2 = x5 + 42. This note extends a result of Mulholland in [8] who gave a description of the set of Q-rational points, i.e., the set of points of degree one over Q on this curve.

引用

页码：59 / 68

页数：10

共 50 条

[1] Algebraic points of small degrees on the affine equation curve y2 = x5
Pall, Moussa
Sall, Oumar
AFRIKA MATEMATIKA, 2018, 29 (7-8) : 1151 - 1157
[2] Algebraic Points of Degree at most 4 on the Affine Curve y2
Sow, E. L. Hadji
INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE, 2023, 18 (04): : 613 - 617
[3] Parameterization of algebraic points of a given degree on the curve of the affine equation y3 = x(x-1)(x-2)(x-3)
Sall, Oumar
Top, Thieyacine
Fall, Moussa
COMPTES RENDUS MATHEMATIQUE, 2010, 348 (21-22) : 1147 - 1150
[4] On the Equation Y2 = X5 + k
Bremner, Andrew
EXPERIMENTAL MATHEMATICS, 2008, 17 (03) : 371 - 374
[5] Algebraic points on the curve of affine equation y2 = x(x- 3)(x- 4)(x- 6)(x -7)
Balde, Boubacar Sidy
Sall, Oumar
AFRIKA MATEMATIKA, 2024, 35 (01)
[6] Sato-Tate distributions of twists of y2 = x5 - x and y2 = x6 + 1
Fite, Francesc
Sutherland, Andrew V.
ALGEBRA & NUMBER THEORY, 2014, 8 (03) : 543 - 585
[7] Ranks in the family of hyperelliptic Jacobians of y2 = x5 + ax
Jedrzejak, Tomasz
JOURNAL OF NUMBER THEORY, 2021, 223 : 35 - 52
[8] Counting points for hyperelliptic curves of type y2 = x5 + ax over finite prime fields
Furukawa, E
Kawazoe, M
Takahashi, T
SELECTED AREAS IN CRYPTOGRAPHY, 2004, 3006 : 26 - 41
[9] Integer points on the curve Y2 = X3 ± pkX
Draziotis, Konstantinos A.
MATHEMATICS OF COMPUTATION, 2006, 75 (255) : 1493 - 1505
[10] Ranks in the family of hyperelliptic Jacobians of y2 = x5 + ax II
Jedrzejak, Tomasz
INTERNATIONAL JOURNAL OF NUMBER THEORY, 2022, 18 (04) : 813 - 837

← 1 2 3 4 5 →