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Prime analogues of the Erdős–Kac theorem for elliptic curves

✍ Scribed by Yu-Ru Liu

Publisher
Elsevier Science
Year
2006
Tongue
English
Weight
146 KB
Volume
119
Category
Article
ISSN
0022-314X

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✦ Synopsis

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 ω(#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) ω(#E(F p ))log log p √ log log p 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(F p ).

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