Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4595627 | Journal of Number Theory | 2006 | 16 Pages |
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).
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Yu-Ru Liu,