Counting Frobenius extensions over local function fields
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917380526964736 |
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| author | Klüners, Jürgen Müller, Raphael |
| author_facet | Klüners, Jürgen Müller, Raphael |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_02152 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Counting Frobenius extensions over local function fields Klüners, Jürgen Müller, Raphael Number Theory 11S20 11S31 11R45 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. |
| title | Counting Frobenius extensions over local function fields |
| topic | Number Theory 11S20 11S31 11R45 |
| url | https://arxiv.org/abs/2604.02152 |