JP Journal of Geometry and Topology

The JP Journal of Geometry and Topology publishes articles in all branches of geometry and topology, with applications to physics. It covers areas such as differential geometry, algebraic topology, and geometric aspects of mathematical physics. Survey articles are also welcome.

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ALGEBRAIC POINTS ON THE CURVES $y^2=ax(x^4+3)$

Authors

  • EL Hadji SOW
  • Moussa Fall
  • Moustapha CAMARA

Keywords:

degree of algebraic points, rational points, algebraic extensions.

DOI:

https://doi.org/10.17654/0972415X23003

Abstract

In this paper, we give an algebraic description of the set of algebraic points of any degree over $\mathbb{Q}$ on hyperelliptic curves $y^2 = ax(x^4 + 3)$. This result extends a result of Bruin [1].

Received: February 1, 2023 
Accepted: March 29, 2023 

References

N. Bruin, On powers as sums of two cubes, International Algorithmic Number Theory Symposium, Springer, Berlin, Heidelberg, 2000.

P. A. Griffiths, Introduction to algebraic curves, Translations of mathematical monographs, American Mathematical Society, Providence, Vol. 76, 1989.

E. H. Sow, P. M. Sarr and O. Sall, Points algébriques de degrés au-plus 5 sur la courbed’ équation affine International Journal of Development Research 11(12) (2021), 52435-52439.

O. Sall, M. Fall and C. M. Coly, Points algébriques de degré donné sur la courbe d’équation affine International Journal of Development Research 6(11) (2016), 10295-10300.

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Published

2023-04-13

Issue

Vol. 29 No. 1 (2023)

Section

Articles

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How to Cite

ALGEBRAIC POINTS ON THE CURVES $y^2=ax(x^4+3)$. (2023). JP Journal of Geometry and Topology, 29(1), 29-34. https://doi.org/10.17654/0972415X23003