Points algébriques de degrés au plus $5$ sur la courbe C d'équation affine y^{2}= 4x^{5}+1

Volume 6, Issue 6, December 2021     |     PP. 73-86      |     PDF (386 K)    |     Pub. Date: December 9, 2021
DOI: 10.54647/mathematics11300    75 Downloads     5691 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
In this work, we determine the set of algebraic points of degree at most Q over on the curve C given by the affine equation y^{2}= 4x^{5}+1. This result extends a result of Andrew R. Booker, Jeroen Sijsling, Andrew V. Sutherland, John Voight and Dan Yasak who described in [1] the set of rational points on this curve

Keywords
Planes curves - Degree of algebraic points - Rationals points - Algebraic extensions - Jacobian-Linear system

Cite this paper
EL Hadji SOW, Moussa FALL, Oumar SALL, Points algébriques de degrés au plus $5$ sur la courbe C d'équation affine y^{2}= 4x^{5}+1 , SCIREA Journal of Mathematics. Volume 6, Issue 6, December 2021 | PP. 73-86. 10.54647/mathematics11300

References

[ 1 ] Andrew R. Booker, Jeroen Sijsling, Andrew V. Sutherland, John Voight and Dan Yasak, (2016). A database of genus-2 curves over the rational numbers. LMS Journal of Computation and Mathematics, 19(A), 235-254.
[ 2 ] P. A. Griffiths, Introduction to algebraic curves, Translations of mathematical monographs volume 76. American Mathematical Society, Providence (1989).
[ 3 ] The LMFDB Collaboration, The L-functions and Modular Forms Database. Available at: http://www.lmfdb.org. [Online; accessed 8 November 2021]
[ 4 ] O. Sall, Points algébriques sur certains quotients de courbes de Fermat, C. R. Acad. Sci. Paris Ser. I 336 (2003) 117-120.
[ 5 ] O. Sall, M. Fall, C. M. Coly, Points algébriques de degré donné sur la courbe d'équation affine , International Journal Of Development Research Vol. 06, Issue, 11, pp. 10295-10300, November, 2016.