Jonathan R. Love

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20232026

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math.NT2026

Generating sets for maximal orders in rational quaternion algebras

Kirsten Eisenträger, Eyal Z. Goren, Annamaria Iezzi +6

Given a maximal order $O$ in a rational definite quaternion algebra, and a prime $ℓ$ coprime to the discriminant of $O$ , this paper considers subsets of $\…

math.NT2026

Arithmetic intersections on non-split Cartan modular curves

Jonathan Love, Elie Studnia, Jan Vonk

Let $p$ be a prime number, and let $Δ_{1}, Δ_{2} < 0$ be two coprime fundamental discriminants. When $p$ splits in $Q (Δ_{1})$ and $Q (Δ_{2})$ the height pairi…

math.NT2024

On $ℓ$ -torsion in degree $ℓ$ superelliptic Jacobians over $F_{q}$

Wanlin Li, Jonathan Love, Eric Stubley

We study the $ℓ$ -torsion subgroup in Jacobians of curves of the form $y^{ℓ} = f (x)$ for irreducible $f (x)$ over a finite field $F_{q}$ of characteristic $p \neq \ell…

math.NT2024

Supersingular elliptic curves, quaternion algebras and applications to cryptography

Eyal Z. Goren, Jonathan R. Love

This paper contains a survey of supersingular isogeny graphs associated to supersingular elliptic curves and their various applications to cryptography. Within limitation of space,…

math.NT2023

Rational configuration problems and a family of curves