M. Stoll

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math.NT2025

Prime numbers and dynamics of the polynomial $x^{2} - 1$

Ivan Penkov, Michael Stoll

Let $n \in Z_{⩾ 2}$ . By $P (n)$ we denote the set of all prime divisors of the integers in the sequence $n, n^{2} - 1, (n^{2} - 1)^{2} - 1, \dots$ . We ask whether the set $P(n)…

math.NT2025

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 $Q$ with Jacobian variety $J$ , given a point $P \in J(\mathbb Q)…

math.NT2025

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…

math.NT2025

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…

math.NT2025

The Generalized Fermat Equation $x^{2} + y^{3} = z^{25}$

Nuno Freitas, Michael Stoll

We consider the generalized Fermat equation (*) $x^{2} + y^{3} = z^{25}$ . Using the known parameterization of the primitive integral solutions to $x^{2} + y^{3} = z^{5}$ (due to Edwards), we…

math.NT2025

Prime order torsion on elliptic curves over number fields. Part I: Asymptotics

Maarten Derickx, Michael Stoll

We study the asymptotics of the set $S (d)$ of possible prime orders of $K$ -rational points on elliptic curves over number fields $K$ of degree $d$ as $d$ tends to infinity. Assumin…

Prime numbers and dynamics of the polynomial x2−1

Determining the rational points on a curve of genus 2 and Mordell-Weil rank 1

On Some Open Cases of a Conjecture of Conrad, Edixhoven and Stein

Formalizing zeta and L-functions in Lean

The Generalized Fermat Equation x2+y3=z25

Prime order torsion on elliptic curves over number fields. Part I: Asymptotics

Prime numbers and dynamics of the polynomial $x^{2} - 1$

The Generalized Fermat Equation $x^{2} + y^{3} = z^{25}$