Parametrization of Algebraic Points of Low Degrees on the Schaeffer Curve

FALL, Moussa

Parametrization of Algebraic Points of Low Degrees on the Schaeffer Curve

Moussa FALL (Department of Mathematics, Faculty of Science and Technology University, Assane Seck, Ziguinchor)

Journal of mathematical sciences and modelling (Online)

2 0

Yıl: 2021 Cilt: 4 Sayı: 2 Sayfa Aralığı: 51 - 55 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022

Parametrization of Algebraic Points of Low Degrees on the Schaeffer Curve

Öz:

In this paper, we give a parametrization of algebraic points of degree at most $4$ over $mathbb{Q}$ on the schaeffer curve $mathcal{C}$ of affine equation : $ y^{2}=x^{5}+1 $. The result extends our previous result which describes in [5] ( Afr. Mat 29:1151-1157, 2018) the set of algebraic points of degree at most $3$ over $mathbb{Q}$ on this curve.

Anahtar Kelime: Rational points Degree of algebraic points Plan curve

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

[1] N. Bruin, M. Stoll, The Mordell-Weil sieve : proving the nonexistence of Rational points on curves, LMS J. Comp. Math., 13 (2010), 272 -306.
[2] R. F. Coleman, Effective Chabauty Duke Math. J. 52(3) (1985), 765-770.
[3] E. F. Schaefer, Computing a Selmer group of a Jacobian using functions on the curve, Mathematische Annalen, 310 (1998), 447–471.
[4] M. J. Klassen, E. F. Schaefer, Arithmetic and geometry of the curve x4 = y3 +1, Acta Arithmetica LXXIV.3 (1996) 241-257.
[5] M. Fall, O. Sall, Ponts alg´ebriques de petit degr´e sur la courbe d’´equation affine y2 = x5 +1, Afr. Mat. 29 (2018) 1151-1157.
[6] O. Sall, Points alg´ebriques sur certains quotients de courbes de Fermat, C. R. Acad. Sci. Paris S´er I 336 (2003) 117-120.
[7] S. Siksek, M. Stoll, Partial descent on hyper elliptic curves and the generalized Fermat equation x3 +y4 +z5 = 0, Bulletin of the LMS 44 (2012) 151 -166

APA	FALL M (2021). Parametrization of Algebraic Points of Low Degrees on the Schaeffer Curve. , 51 - 55.
Chicago	FALL Moussa Parametrization of Algebraic Points of Low Degrees on the Schaeffer Curve. (2021): 51 - 55.
MLA	FALL Moussa Parametrization of Algebraic Points of Low Degrees on the Schaeffer Curve. , 2021, ss.51 - 55.
AMA	FALL M Parametrization of Algebraic Points of Low Degrees on the Schaeffer Curve. . 2021; 51 - 55.
Vancouver	FALL M Parametrization of Algebraic Points of Low Degrees on the Schaeffer Curve. . 2021; 51 - 55.
IEEE	FALL M "Parametrization of Algebraic Points of Low Degrees on the Schaeffer Curve." , ss.51 - 55, 2021.
ISNAD	FALL, Moussa. "Parametrization of Algebraic Points of Low Degrees on the Schaeffer Curve". (2021), 51-55.

APA	FALL M (2021). Parametrization of Algebraic Points of Low Degrees on the Schaeffer Curve. Journal of mathematical sciences and modelling (Online), 4(2), 51 - 55.
Chicago	FALL Moussa Parametrization of Algebraic Points of Low Degrees on the Schaeffer Curve. Journal of mathematical sciences and modelling (Online) 4, no.2 (2021): 51 - 55.
MLA	FALL Moussa Parametrization of Algebraic Points of Low Degrees on the Schaeffer Curve. Journal of mathematical sciences and modelling (Online), vol.4, no.2, 2021, ss.51 - 55.
AMA	FALL M Parametrization of Algebraic Points of Low Degrees on the Schaeffer Curve. Journal of mathematical sciences and modelling (Online). 2021; 4(2): 51 - 55.
Vancouver	FALL M Parametrization of Algebraic Points of Low Degrees on the Schaeffer Curve. Journal of mathematical sciences and modelling (Online). 2021; 4(2): 51 - 55.
IEEE	FALL M "Parametrization of Algebraic Points of Low Degrees on the Schaeffer Curve." Journal of mathematical sciences and modelling (Online), 4, ss.51 - 55, 2021.
ISNAD	FALL, Moussa. "Parametrization of Algebraic Points of Low Degrees on the Schaeffer Curve". Journal of mathematical sciences and modelling (Online) 4/2 (2021), 51-55.