Orders of CM elliptic curves modulo p with at most two primes

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Title:	Orders of CM elliptic curves modulo p with at most two primes
Author:	Iwaniec, Henryk; Jiménez Urroz, Jorge
Other authors:	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV; Universitat Politècnica de Catalunya. TN - Teoria de Nombres
Abstract:	We prove the analog of Koblitz conjecture when replacing primes by almost prime numbers and considering elliptic curves with complex multiplication. In other words for infinitely many primes $p$, (given in a quantitative way describe in the paper), the reduction of an elliptic curve $E$ with complex multiplication has order of size an almost prime number.
Subject(s):	Àrees temàtiques de la UPC::Matemàtiques i estadística Number theory elliptic curves sieve Koblitz conjecture Sieve, Mètode de Nombres, Teoria dels Classificació AMS::11 Number theory
Rights:	Attribution-NonCommercial-NoDerivs 2.5 Spain http://creativecommons.org/licenses/by-nc-nd/2.5/es/
Document type:	Article
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