CYCLICITY OF CM ELLIPTIC CURVES MODULO p
نویسنده
چکیده
Let E be an elliptic curve defined over Q and with complex multiplication. For a prime p of good reduction, let E be the reduction of E modulo p. We find the density of the primes p ≤ x for which E(Fp) 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.
منابع مشابه
On the cyclicity of the group of Fp-rational points of non-CM elliptic curves
ABSTRACT: Let E be an elliptic curve defined over Q and without complex multiplication. For a prime p of good reduction, let E be the reduction of E modulo p. Assuming that certain Dedekind zeta functions have no zeros in Re(s) > 3/4, we determine how often E(Fp) is a cyclic group. This result was previously obtained by J. -P. Serre using the full Generalized Riemann Hypothesis for the same Ded...
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