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An analogue of the Siegel-Walfisz theorem for the cyclicity of CM elliptic curves modp

✍ Scribed by Amir Akbary; V. Kumar Murty


Book ID
107690488
Publisher
Indian National Science Academy
Year
2010
Tongue
English
Weight
147 KB
Volume
41
Category
Article
ISSN
0019-5588

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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 Ο‰(#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) Ο‰(#E(F p ))log log p