Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Equidistribution of Hecke points on the supersingular module

Author: Ricardo Menares
Journal: Proc. Amer. Math. Soc. 140 (2012), 2687-2691
MSC (2010): Primary 11F11, 14H52; Secondary 11F32
Published electronically: December 29, 2011
MathSciNet review: 2910756
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: For a fixed prime $ p$, we consider the (finite) set of supersingular elliptic curves over $ \overline {\mathbb{F}}_p$. Hecke operators act on this set. We compute the asymptotic frequence with which a given supersingular elliptic curve visits another under this action.

References [Enhancements On Off] (What's this?)

  • 1. Laurent Clozel and Emmanuel Ullmo, Équidistribution des points de Hecke, Contributions to automorphic forms, geometry, and number theory, Johns Hopkins Univ. Press, Baltimore, MD, 2004, pp. 193–254 (French). MR 2058609
  • 2. Pierre Deligne, La conjecture de Weil. I, Inst. Hautes Études Sci. Publ. Math. 43 (1974), 273–307 (French). MR 0340258
  • 3. M. Eichler, The basis problem for modular forms and the traces of the Hecke operators, Modular functions of one variable, I (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972) Springer, Berlin, 1973, pp. 75–151. Lecture Notes in Math., Vol. 320. MR 0485698
  • 4. Benedict H. Gross, Heights and the special values of 𝐿-series, Number theory (Montreal, Que., 1985) CMS Conf. Proc., vol. 7, Amer. Math. Soc., Providence, RI, 1987, pp. 115–187. MR 894322
  • 5. Toshitsune Miyake, Modular forms, Reprint of the first 1989 English edition, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2006. Translated from the 1976 Japanese original by Yoshitaka Maeda. MR 2194815

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 11F11, 14H52, 11F32

Retrieve articles in all journals with MSC (2010): 11F11, 14H52, 11F32

Additional Information

Ricardo Menares
Affiliation: Facultad de Matematicas, Pontificia Universidad Católica de Chile, Avda. Vicuña Mackenna 4860, Santiago, Chile

Received by editor(s): January 27, 2011
Received by editor(s) in revised form: March 18, 2011
Published electronically: December 29, 2011
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society