On the cyclicity of the group of Fp-rational points of non-CM elliptic curves

[摘要] Let E be an elliptic curve defined over Q and without complex multiplication. For a prime p of good reduction, let (E) over bar 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) over bar (F-p) is a cyclic group. This result was previously obtained by J.-P. Serve using the full Generalized Riemann Hypothesis for the same Dedekind zeta functions considered by us. (C) 2002 Elsevier Science (USA).

[发布日期] 2002-10-01