Uniform bounds for rational points on hyperelliptic fibrations
Number Theory
2021-09-28 v2
Abstract
We apply a variant of the square-sieve to produce a uniform upper bound for the number of rational points of bounded height on a family of surfaces that admit a fibration over the projective line, whose general fibre is a hyperelliptic curve.
Cite
@article{arxiv.2007.14182,
title = {Uniform bounds for rational points on hyperelliptic fibrations},
author = {Dante Bonolis and Tim Browning},
journal= {arXiv preprint arXiv:2007.14182},
year = {2021}
}
Comments
30 pages; we have added an appendix that describes Hooley's method of moments for exponential sums in more detail