179 citations · 759 across the 49 of their papers we have counts for
4 papers · 1 filter
On the Number of Rational Iterated Pre-images of the Origin Under Quadratic Dynamical Systems
Xander Faber, Benjamin Hutz, Michael Stoll
For a quadratic endomorphism of the affine line defined over the rationals, we consider the problem of bounding the number of rational points that eventually land at the origin aft…
Documentation for the ratpoints program
Michael Stoll
This note explains how to obtain, install, and use the ratpoints program. The program finds rational points up to a specified height on hyperelliptic curves using a highly optimize…
Rational 6-cycles under iteration of quadratic polynomials
Michael Stoll
We present a proof, which is conditional on the Birch and Swinnerton-Dyer Conjecture for a specific abelian variety, that there do not exist rational numbers x and c such that x ha…
Two-cover descent on hyperelliptic curves
Nils Bruin, Michael Stoll
We describe an algorithm that determines a set of unramified covers of a given hyperelliptic curve, with the property that any rational point will lift to one of the covers. In par…