Uniform bounds for rational points on hyperelliptic fibrations

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.

arXiv comment30 pages; we have added an appendix that describes Hooley's method of moments for exponential sums in more detail