
تعداد نشریات | 26 |
تعداد شمارهها | 399 |
تعداد مقالات | 3,523 |
تعداد مشاهده مقاله | 5,417,167 |
تعداد دریافت فایل اصل مقاله | 3,702,981 |
Describing families of algebraic points of given degree on a hyperelliptic curve | ||
Journal of Finsler Geometry and its Applications | ||
دوره 6، شماره 1، 2025، صفحه 83-91 اصل مقاله (325.98 K) | ||
نوع مقاله: Original Article | ||
شناسه دیجیتال (DOI): 10.22098/jfga.2025.16876.1147 | ||
نویسنده | ||
Mohamadou Mor Diogou Diallo* | ||
Department of Mathematics, Assane Seck University of Ziguinchor Ziguinchor, Senegal | ||
چکیده | ||
In this paper, we give a parametrization of the set of algebraic points of degree at most l over Q on the hyperelliptic curve y2 = x(x2 + x - 4)(x2 - x + 45) This curve was studied by Bruin and Flynn in [4] where the heights explicitly described the set of rational points, i.e. C(1)(Q). Drawing on the work of Arnth-Jensen and Flynn based on [2] and one of Abel-Jacobi's fundamental theorems in [1, 8], we extend the results of [4] to algebraic points of any degree which we denote C(l)(Q). | ||
کلیدواژهها | ||
Mordell-Weill group؛ Rational Points؛ Jacobian؛ Galois Conjugate؛ Linear Systems | ||
مراجع | ||
1. E. Arbarello, M. Cornalba, P. A. Griffiths and J. Harris. The Basic Results of the BrillNoether Theory, Geometry of Algebraic Curves, 133 (3) (1985), 203{224. 2. A. Arnth-Jensen and E. V. Flynn, Non-trivial in the Jacobian of an infinite family of curves of genus 2, Journal de th´eorie des nombres de Bordeaux, 21 (1) (2009), 1-13. 3. A. Borel and J. P. Serre, Le th´eor´eme de Riemann-Roch, Bultin de la Soci´et´e math´ematiques de france, 86 (1958), 97-136. 4. N. Bruin and E. V. Flynn, Exhibiting SHA [2] on hyperelliptic Jacobians, Journal of Number Theory, 118 (2) (2006), 266-291. 5. M. Coppens and G. Martens, Secant spaces and Clifford’s theorem, Compositio Mathematica, 78 (2) (1991), 193-212. 6. M. Fall, M. M. D.Diallo and C. M. Coly, Algebraic Points of any Given Degree on the Affine Curves y2 = x(x + 2p)(x + 4p)(x2 - 8p2), Journal of Contemporary Applied Mathematics, 13 (1) (2023), 11-23. 7. G. Faltings, Finiteness Theorems for Abelian Varieties over Number Fields, Arithmetic Geometry, 1986. 8. P. A. Griffiths, Introduction to algebraic curves: Translations of mathematical monographs, American Mathematical Society, Providence, RI, 76 (1989). 9. M. Gromov and M. A. Shubin, The Riemann-Roch theorem for elliptic operators, IM Gelfand Seminar part, 1 (1993). 10. M. M. D. Diallo, Explicit family of algebraic points of given degree of the curve family Cq, Journal of Advanced Mathematical Studies, 17 (4) (2024), 444-450. 11. P. Vojta, Siegel’s theorem in the compact case, Annals of Mathematics, 133 (3) (1991),509-548. | ||
آمار تعداد مشاهده مقاله: 54 تعداد دریافت فایل اصل مقاله: 50 |