Prime analogues of the Erdős–Kac theorem for elliptic curves Original Research Article

Let image be an elliptic curve. For a prime p of good reduction, let image be the set of rational points defined over the finite field image. We denote by image, the number of distinct prime divisors of image. We prove that the quantity (assuming the GRH if E is non-CM)image distributes normally. This result can be viewed as a “prime analogue” of the Erdős–Kac theorem. We also study the normal distribution of the number of distinct prime factors of the exponent of image.