179 citations · 759 across the 49 of their papers we have counts for
5 papers · 2 filters
On a problem of Hajdu and Tengely
Samir Siksek, Michael Stoll
We prove a result that finishes the study of primitive arithmetic progressions consisting of squares and fifth powers that was carried out by Hajdu and Tengely in a recent paper: T…
Reduction theory of point clusters in projective space
Michael Stoll
In this paper, we generalise results obtained earlier by John Cremona and the author on the reduction theory of binary forms, which describe positive zero-cycles in P^1, to positiv…
Minimisation and reduction of 2-, 3- and 4-coverings of elliptic curves
John Cremona, Tom Fisher, Michael Stoll
In this paper we consider models for genus one curves of degree n for n = 2, 3 and 4, which arise in explicit n-descent on elliptic curves. We prove theorems on the existence of mi…
The Mordell-Weil sieve: Proving non-existence of rational points on curves
Nils Bruin, Michael Stoll
We discuss the Mordell-Weil sieve as a general technique for proving results concerning rational points on a given curve. In the special case of curves of genus 2, we describe quit…
On the average number of rational points on curves of genus 2
Michael Stoll
Based on computational evidence, we formulate a number of conjectures on the distribution of rational points on curves of genus 2 over the rational numbers, in terms of the size of…