Counting Frobenius extensions over local function fields Klüners, Jürgen Müller, Raphael 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. 2026 info:eu-repo/semantics/preprint doc-type:preprint text http://purl.org/coar/resource_type/c_816b https://ris.uni-paderborn.de/record/65358 Klüners J, Müller R. Counting Frobenius extensions over local function fields. <i>arXiv:260402152</i>. Published online 2026. eng info:eu-repo/semantics/altIdentifier/arxiv/2604.02152 info:eu-repo/semantics/closedAccess