Johann Franke

collaborators

3 papers

math.NT2025

Asymptotics for the Enumeration of Commuting Matrices over Finite Fields

Kathrin Bringmann, Shane Chern, Johann Franke +1

We give asymptotic expressions for the number of commuting matrices over finite fields. For this, we use product expansions for the corresponding generating functions.

math.NT2024

Asymptotics of commuting $ℓ$ -tuples in symmetric groups and log-concavity

Kathrin Bringmann, Johann Franke, Bernhard Heim

Denote by $N_{ℓ} (n)$ the number of $ℓ$ -tuples of elements in the symmetric group $S_{n}$ with commuting components, normalized by the order of $S_{n}$ . In this paper, we prove as…

math.NT2023

On the Proportion of Coprime Fractions in Number Fields

Walter Bridges, Johann Franke, Johann Christian Stumpenhusen

In this paper we determine the asymptotic density of coprime fractions in those of the reduced fractions of number fields. When ordered by norms of denominators, we count a fractio…

Asymptotics for the Enumeration of Commuting Matrices over Finite Fields

Asymptotics of commuting ℓ-tuples in symmetric groups and log-concavity

On the Proportion of Coprime Fractions in Number Fields

Asymptotics of commuting $ℓ$ -tuples in symmetric groups and log-concavity