Points algébriques sur une courbe hyperelliptique de Nils Bruin

Volume 8, Issue 4, August 2023     |     PP. 130-138      |     PDF (1195 K)    |     Pub. Date: September 18, 2023
DOI: 10.54647/mathematics110421    76 Downloads     30834 Views  

Author(s)

El Hadji SOW, Laboratoire de Mathématiques et Applications (L.M.A.) Université Assane SECK Ziguinchor, Senegal
Moussa FALL, Laboratoire de Mathématiques et Applications (L.M.A.) Université Assane SECK Ziguinchor, Senegal
Oumar SALL, Laboratoire de Mathématiques et Applications (L.M.A.) Université Assane SECK Ziguinchor, Senegal

Abstract
We give the set of algebraic points of degree ≤5 over Q on the hyperelliptic curveC: y²=6x(x^4+3). This result extends a previous result of Bruin of who described in [1] the set of Q-rational points on this curve.

Keywords
Degree of algebraic points - Rational points - Algebraic extensions - Jacobian.

Cite this paper
El Hadji SOW, Moussa FALL, Oumar SALL, Points algébriques sur une courbe hyperelliptique de Nils Bruin , SCIREA Journal of Mathematics. Volume 8, Issue 4, August 2023 | PP. 130-138. 10.54647/mathematics110421

References

[ 1 ] N. Bruin, On powers as sums of two cubes, International Algorithmic Number Theory Symposium. Springer, Berlin, Heidelberg, 2000.
[ 2 ] P. A. Griffiths, Introduction to algebraic curves, Translations of mathematical monographs volume 76. American Mathematical Society, Providence, 1989.
[ 3 ] M. Hindry and J. H. Silverman, Diophantie geometry, an introduction, springer verlage,2000.
[ 4 ] J. TH. Mulholland, Elliptic curves with rational 2-torsion and related ternary Diophantine equations. ProQuest LLC. Ann Arbor, MI, 2006.
[ 5 ] E. H. Sow, M. Fall, O. Sall, Points algébriques de degrésau-plus 5 sur la courbe d'équation affine , SCIREA Journal of Mathematics, Volume 6, Issue 6, 2021.