Fabian Gundlach

activity

20242026

collaborators

8 papers

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, BÃ©ranger 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.AG2026

On matrices commuting with their Frobenius

Fabian Gundlach, BÃ©ranger Seguin

The Frobenius of a matrix $M$ with coefficients in $F ˉ_{p}$ is the matrix $I ¨ (M)$ obtained by raising each coefficient to the $p$ -th power. We consider the question of c…

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 abelian extensions by Artin-Schreier conductor

Fabian Gundlach

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

math.NT2025

Asymptotics of extensions of simple $Q$ -algebras

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

On matrices commuting with their Frobenius

The structure of the double discriminant

Counting abelian extensions by Artin-Schreier conductor

Asymptotics of extensions of simple Q-algebras

Asymptotics of extensions of simple $Q$ -algebras