preprint Jürgen Klüners author 21202 Raphael Müller author 55246 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 eng 2604.02152 Klüners, Jürgen, and Raphael Müller. “Counting Frobenius Extensions over Local Function Fields.” <i>ArXiv:2604.02152</i>, 2026. J. Klüners and R. Müller, “Counting Frobenius extensions over local function fields,” <i>arXiv:2604.02152</i>. 2026. Klüners J, Müller R. Counting Frobenius extensions over local function fields. <i>arXiv:260402152</i>. Published online 2026. Klüners, J., &#38; Müller, R. (2026). Counting Frobenius extensions over local function fields. In <i>arXiv:2604.02152</i>. @article{Klüners_Müller_2026, title={Counting Frobenius extensions over local function fields}, journal={arXiv:2604.02152}, author={Klüners, Jürgen and Müller, Raphael}, year={2026} } J. Klüners, R. Müller, ArXiv:2604.02152 (2026). Klüners, Jürgen, and Raphael Müller. “Counting Frobenius Extensions over Local Function Fields.” <i>ArXiv:2604.02152</i>, 2026. 653582026-04-07T08:13:59Z2026-04-07T08:14:45Z