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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
Posted:
December 29, 2011
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Abstract: For a fixed prime , we consider the (finite) set of supersingular elliptic curves over . Hecke operators act on this set. We compute the asymptotic frequence with which a given supersingular elliptic curve visits another under this action.
References
- 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 (2005f:11090)
- 2.
Pierre
Deligne, La conjecture de Weil. I, Inst. Hautes Études
Sci. Publ. Math. 43 (1974), 273–307 (French). MR 0340258
(49 #5013)
- 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
(58 #5521a)
- 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
(89c:11082)
- 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
(2006g:11084)
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Additional Information
Ricardo Menares
Affiliation:
Facultad de Matematicas, Pontificia Universidad Católica de Chile, Avda. Vicuña Mackenna 4860, Santiago, Chile
Email:
remenares@mat.puc.cl
DOI:
http://dx.doi.org/10.1090/S0002-9939-2011-11148-1
PII:
S 0002-9939(2011)11148-1
Received by editor(s):
January 27, 2011
Received by editor(s) in revised form:
March 18, 2011
Posted:
December 29, 2011
Communicated by:
Matthew A. Papanikolas
Article copyright:
© Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain after
28 years from publication.
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