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On the Cyclicity of the Group ofFp-Rational Points of Non-CM Elliptic Curves

Authors
Journal
Journal of Number Theory
0022-314X
Publisher
Elsevier
Publication Date
Volume
96
Issue
2
Identifiers
DOI: 10.1006/jnth.2002.2789

Abstract

Abstract Let E be an elliptic curve defined over Q and without complex multiplication. For a prime p of good reduction, let Ē be the reduction of E modulo p. Assuming that certain Dedekind zeta functions have no zeros in Re( s)>3/4, we determine how often Ē( F p ) is a cyclic group. This result was previously obtained by J.-P. Serre using the full Generalized Riemann Hypothesis for the same Dedekind zeta functions considered by us.

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