Article ID Journal Published Year Pages File Type
4595627 Journal of Number Theory 2006 16 Pages PDF
Abstract

Let E/QE/Q be an elliptic curve. For a prime p   of good reduction, let E(Fp)E(Fp) be the set of rational points defined over the finite field FpFp. We denote by ω(#E(Fp))ω(#E(Fp)), the number of distinct prime divisors of #E(Fp)#E(Fp). We prove that the quantity (assuming the GRH if E is non-CM)ω(#E(Fp))−loglogploglogp 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 E(Fp)E(Fp).

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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