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Year 2021, Volume: 4 Issue: 2, 51 - 55, 31.08.2021
https://doi.org/10.33187/jmsm.931258

Abstract

References

  • [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

Parametrization of Algebraic Points of Low Degrees on the Schaeffer Curve

Year 2021, Volume: 4 Issue: 2, 51 - 55, 31.08.2021
https://doi.org/10.33187/jmsm.931258

Abstract

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.

References

  • [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
There are 7 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Moussa Fall 0000-0003-3880-7603

Publication Date August 31, 2021
Submission Date May 2, 2021
Acceptance Date August 19, 2021
Published in Issue Year 2021 Volume: 4 Issue: 2

Cite

APA Fall, M. (2021). Parametrization of Algebraic Points of Low Degrees on the Schaeffer Curve. Journal of Mathematical Sciences and Modelling, 4(2), 51-55. https://doi.org/10.33187/jmsm.931258
AMA Fall M. Parametrization of Algebraic Points of Low Degrees on the Schaeffer Curve. Journal of Mathematical Sciences and Modelling. August 2021;4(2):51-55. doi:10.33187/jmsm.931258
Chicago Fall, Moussa. “Parametrization of Algebraic Points of Low Degrees on the Schaeffer Curve”. Journal of Mathematical Sciences and Modelling 4, no. 2 (August 2021): 51-55. https://doi.org/10.33187/jmsm.931258.
EndNote Fall M (August 1, 2021) Parametrization of Algebraic Points of Low Degrees on the Schaeffer Curve. Journal of Mathematical Sciences and Modelling 4 2 51–55.
IEEE M. Fall, “Parametrization of Algebraic Points of Low Degrees on the Schaeffer Curve”, Journal of Mathematical Sciences and Modelling, vol. 4, no. 2, pp. 51–55, 2021, doi: 10.33187/jmsm.931258.
ISNAD Fall, Moussa. “Parametrization of Algebraic Points of Low Degrees on the Schaeffer Curve”. Journal of Mathematical Sciences and Modelling 4/2 (August 2021), 51-55. https://doi.org/10.33187/jmsm.931258.
JAMA Fall M. Parametrization of Algebraic Points of Low Degrees on the Schaeffer Curve. Journal of Mathematical Sciences and Modelling. 2021;4:51–55.
MLA Fall, Moussa. “Parametrization of Algebraic Points of Low Degrees on the Schaeffer Curve”. Journal of Mathematical Sciences and Modelling, vol. 4, no. 2, 2021, pp. 51-55, doi:10.33187/jmsm.931258.
Vancouver Fall M. Parametrization of Algebraic Points of Low Degrees on the Schaeffer Curve. Journal of Mathematical Sciences and Modelling. 2021;4(2):51-5.

Cited By

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https://doi.org/10.2478/aupcsm-2023-0003

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