The distribution of the number of points modulo an integer on elliptic curves over finite fields
Number Theory
2011-02-01 v3 Algebraic Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.0902.4332,
title = {The distribution of the number of points modulo an integer on elliptic curves over finite fields},
author = {Wouter Castryck and Hendrik Hubrechts},
journal= {arXiv preprint arXiv:0902.4332},
year = {2011}
}
Comments
21 pages; completely rewritten because of an error in the previous version