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Abstract:

Watkins’ conjecture asserts that for a rational elliptic curve E the degree of the modular parametrization is divisible by 2r, where r is the rank of E. In this paper, we prove that if the modular degree is odd, then E has rank zero. Moreover, we prove that the conjecture holds for all rank two rational elliptic curves of prime conductor and positive discriminant. © 2017 American Mathematical Society.

Registro:

Documento: Artículo
Título:On a special case of Watkins’ conjecture
Autor:Kazalicki, M.; Kohen, D.
Filiación:Department of Mathematics, University of Zagreb, Bijenička cesta 30, Zagreb, 10000, Croatia
Departamento de Matemática, Universidad de Buenos Aires and IMAS-CONICET, Ciudad Universitaria, Buenos Aires, Argentina
Año:2017
Volumen:146
Número:2
Página de inicio:541
Página de fin:545
DOI: http://dx.doi.org/10.1090/proc/13759
Título revista:Proceedings of the American Mathematical Society
Título revista abreviado:Proc. Am. Math. Soc.
ISSN:00029939
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v146_n2_p541_Kazalicki

Referencias:

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  • Darmon, H., Rational points on modular elliptic curves, CBMS Regional Conference Series in Mathematics (2004) Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 101. , MR2020572
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  • Benedict, H., Gross and Stephen S. Kudla, Heights and the central critical values of triple product L-functions (1992) Compositio Math, 81 (2), pp. 143-209. , MR1145805
  • Kazalicki, M., Kohen, D., Supersingular zeros of divisor polynomials of elliptic curves of prime conductor (2017) Res. Math. Sci, 4
  • Mestre, J.-F., La, M.D.G., Exemples et applications (French), Proceedings of the international conference on class numbers and fundamental units of algebraic number fields (Katata (1986) Nagoya Univ., Nagoya, pp. 217-242. , MR891898
  • Stein, W., Watkins, M., Modular parametrizations of Neumann-Setzer elliptic curves (2004) Int. Math. Res. Not, 27, pp. 1395-1405. , MR2052021
  • Yazdani, S., Modular abelian varieties of odd modular degree (2011) Algebra Number Theory, 5 (1), pp. 37-62. , MR2833784
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Citas:

---------- APA ----------
Kazalicki, M. & Kohen, D. (2017) . On a special case of Watkins’ conjecture. Proceedings of the American Mathematical Society, 146(2), 541-545.
http://dx.doi.org/10.1090/proc/13759
---------- CHICAGO ----------
Kazalicki, M., Kohen, D. "On a special case of Watkins’ conjecture" . Proceedings of the American Mathematical Society 146, no. 2 (2017) : 541-545.
http://dx.doi.org/10.1090/proc/13759
---------- MLA ----------
Kazalicki, M., Kohen, D. "On a special case of Watkins’ conjecture" . Proceedings of the American Mathematical Society, vol. 146, no. 2, 2017, pp. 541-545.
http://dx.doi.org/10.1090/proc/13759
---------- VANCOUVER ----------
Kazalicki, M., Kohen, D. On a special case of Watkins’ conjecture. Proc. Am. Math. Soc. 2017;146(2):541-545.
http://dx.doi.org/10.1090/proc/13759