Prime analogues of the Erdos-Kac theorem for elliptic curves

Let E/Q be an elliptic curve. For a prime p of good reduction, let E(F-p) be the set of rational points defined over the finite field F-P We denote by omega(#E(F-p)), the number of distinct prime divisors of #E(F-p). We prove that the quantity (assuming the GRH if E is non-CM) [GRAPHICS] distributes normally. This result can be viewed as a "prime analogue" of the Erdos-Kac theorem. We also study the normal distribution of the number of distinct prime factors of the exponent of E(F-p). (c) 2005 Elsevier Inc. All rights reserved.