8 papers
Determining the rational points on a curve of genus 2 and Mordell-Weil rank 1
Michael Stoll
We explain how one can efficiently determine the (finite) set of rational points on a curve of genus 2 over with Jacobian variety , given a point $P \in J(\mathbb Q)…
Coarse length can be unbounded in 3-step nilpotent Lie groups
Michael Stoll
In "On the asymptotics of the growth of 2-step nilpotent groups" (J. London Math. Soc. (2), 58 (1998)), we remarked that, contrary to 2-step nilpotent simply connected Lie groups,…
The Generalized Fermat Equation
Nuno Freitas, Michael Stoll
We consider the generalized Fermat equation (*) . Using the known parameterization of the primitive integral solutions to (due to Edwards), we…
Prime order torsion on elliptic curves over number fields. Part I: Asymptotics
Maarten Derickx, Michael Stoll
We study the asymptotics of the set of possible prime orders of -rational points on elliptic curves over number fields of degree as tends to infinity. Assumin…
On Some Open Cases of a Conjecture of Conrad, Edixhoven and Stein
Davide De Leo, Michael Stoll
Let \( p \geq 5 \) be a prime. In 2003 Conrad, Edixhoven, and Stein conjectured that the rational torsion subgroup of the modular Jacobian \( J_1(p) \) coincides with the rational…
Formalizing zeta and L-functions in Lean
David Loeffler, Michael Stoll
The Riemann zeta function, and more generally the L-functions of Dirichlet characters, are among the central objects of study in number theory. We report on a project to formalize…
Prime numbers and dynamics of the polynomial
Ivan Penkov, Michael Stoll
Let . By we denote the set of all prime divisors of the integers in the sequence . We ask whether the set $P(n)…
Complete verification of strong BSD for many modular abelian surfaces over
Timo Keller, Michael Stoll
We develop the theory and algorithms necessary to be able to verify the strong Birch--Swinnerton-Dyer Conjecture for absolutely simple modular abelian varieties over .…