The distribution of the number of points modulo an integer on elliptic curves over finite fields

Details The distribution of the number of points modulo an integer on elliptic curves over finite fields The distribution of the number of points modulo an integer on elliptic curves over finite fields

2009-02-25

arxiv.org/abs/0902.4332v3

Mathematics

Number Theory

21 pages; completely rewritten because of an error in the previous version

Scientific paper

Let F be a finite field and let b and N be integers. We prove explicit
estimates for the probability that the number of rational points on a randomly
chosen elliptic curve E over F equals b modulo N. The underlying tool is an
equidistribution result on the action of Frobenius on the N-torsion subgroup of
E. Our results subsume and extend previous work by Achter and Gekeler.

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