On curves over finite fields with Jacobians of small exponent
Number Theory
2008-11-06 v3
Abstract
We show that finite fields over which there is a curve of a given genus g with its Jacobian having a small exponent, are very rare. This extends a recent result of W. Duke in the case g=1. We also show when g=1 or g=2 that our bounds are best possible.
Cite
@article{arxiv.math/0607474,
title = {On curves over finite fields with Jacobians of small exponent},
author = {Kevin Ford and Igor Shparlinski},
journal= {arXiv preprint arXiv:math/0607474},
year = {2008}
}
Comments
V3. Small corrections; references updated