Harun Kir

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20222026

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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.AG2026

The Number of Curves of Genus 2 with a Given Refined Humbert Invariant

Ernst Kani, Harun Kir

Let $C / K$ be a curve of genus 2 over an algebraically closed field $K$ . Every such curve comes equipped with a canonical quadratic form $q_{C}$ called its refined Humbert invariant.…

math.NT2026

Constructing genus 2 curves with given refined Humbert invariants

Harun Kir

In 1994, Kani introduced an algebraic version of the Humbert invariant, known as the refined Humbert invariant. This invariant q_C is a positive definite quadratic form attached to…