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Cyclicity of CM elliptic curves modulo  |
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| Authors: | Alina Carmen Cojocaru |
| Affiliation: | Department of Mathematics and Statistics, Queen's University, Kingston, Ontario, Canada, K7L 3N6 |
| 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. |
| Keywords: | Cyclicity of elliptic curves modulo $p$ complex multiplication applications of sieve methods |
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