Cyclicity of CM elliptic curves modulo
Author:
Alina Carmen Cojocaru
Journal:
Trans. Amer. Math. Soc. 355 (2003), 26512662
MSC (2000):
Primary 11G05; Secondary 11N36, 11G15, 11R45
Published electronically:
March 14, 2003
MathSciNet review:
1975393
Fulltext PDF Free Access
Abstract 
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Abstract: Let be an elliptic curve defined over and with complex multiplication. For a prime of good reduction, let be the reduction of modulo We find the density of the primes for which is a cyclic group. An asymptotic formula for these primes had been obtained conditionally by J.P. Serre in 1976, and unconditionally by Ram Murty in 1979. The aim of this paper is to give a new simpler unconditional proof of this asymptotic formula and also to provide explicit error terms in the formula.
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Additional Information
Alina Carmen Cojocaru
Affiliation:
Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario, Canada, K7L 3N6
Address at time of publication:
The Fields Institute for Research in Mathematical Sciences, 222 College Street, Toronto, Ontario, M5T 3J1, Canada
Email:
alina@mast.queensu.ca, alina@fields.utoronto.ca
DOI:
http://dx.doi.org/10.1090/S0002994703032835
PII:
S 00029947(03)032835
Keywords:
Cyclicity of elliptic curves modulo $p$,
complex multiplication,
applications of sieve methods
Received by editor(s):
July 24, 2002
Received by editor(s) in revised form:
December 4, 2002
Published electronically:
March 14, 2003
Additional Notes:
Research partially supported by an Ontario Graduate Scholarship
Article copyright:
© Copyright 2003 American Mathematical Society
