Fabian Gundlach

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20242026

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math.NT2026

Multivariate counting of wild abelian extensions

Fabian Gundlach

Let $K$ be a global function field of characteristic~ $p$ and let $G$ be a finite abelian group of exponent $p^{e}$ . We show that the multivariate generating function counting sub- $G$ …

math.NT2026

Lifts of unramified twists and local-global principles

Fabian Gundlach, Béranger Seguin

We prove that two-step nilpotent $p$ -extensions of rational global function fields of characteristic $p$ satisfy a quantitative local-global principle when they are counted accordi…

math.NT2025

The structure of the double discriminant

Theresa C. Anderson, Ufuoma V. Asarhasa, Adam Bertelli +2

For a polynomial $f (x) = \sum_{i = 0}^{n} a_{i} x^{i}$ , we study the double discriminant $D D_{n, k} = disc_{a_{k}} disc_{x} f (x)$ . This object has been well studie…

math.NT2025

Counting two-step nilpotent wildly ramified extensions of function fields

Fabian Gundlach, Béranger Seguin

We study the asymptotic distribution of wildly ramified extensions of function fields in characteristic $p > 2$ , focusing on (certain) $p$ -groups of nilpotency class at most $2$ . R…

math.NT2024

Counting abelian extensions by Artin-Schreier conductor

Fabian Gundlach

Let $G$ be a finite abelian $p$ -group. We count étale $G$ -extensions of global rational function fields $F_{q} (T)$ of characteristic $p$ by the degree of what we call their A…

math.NT2024

Sampling cubic rings

Fabian Gundlach

We explain how to construct a uniformly random cubic integral domain $S$ of given signature with $∣ disc (S) ∣ \leq T$ in expected time $O (lo g T)$ .

math.NT2024

Asymptotics of extensions of simple $Q$ -algebras

Fabian Gundlach, Béranger Seguin

We answer various questions concerning the distribution of extensions of a given central simple algebra $K$ over a number field. Specifically, we give asymptotics for the count of…

Multivariate counting of wild abelian extensions

Lifts of unramified twists and local-global principles

The structure of the double discriminant

Counting two-step nilpotent wildly ramified extensions of function fields

Counting abelian extensions by Artin-Schreier conductor

Sampling cubic rings

Asymptotics of extensions of simple Q-algebras

Asymptotics of extensions of simple $Q$ -algebras