Counting Frobenius extensions over local function fields
Number Theory
2026-04-03 v1
Abstract
We determine the asymptotic growth of extensions of local function fields of characteristic p counted by discriminant, where the Galois group is a subgroup of the affine group AGL_1(p). More general, we solve the corresponding counting problems for all groups which arise in a tower of a cyclic extension of order p over a cyclic extension of degree d coprime to p. This in particular give answers for certain non-abelian groups including S_3, dihedral groups of order 2p, and many Frobenius groups.
Cite
@article{arxiv.2604.02152,
title = {Counting Frobenius extensions over local function fields},
author = {Jürgen Klüners and Raphael Müller},
journal= {arXiv preprint arXiv:2604.02152},
year = {2026}
}