The conductor density of local function fields with abelian Galois group

Jürgen Klüners; Raphael Müller

The conductor density of local function fields with abelian Galois group

Number Theory 2019-11-01 v3

Authors: Jürgen Klüners , Raphael Müller

Abstract

We give an exact formula for the number of $G$ -extensions of local function fields $\mathbb{F}_q((t))$ for finite abelian groups $G$ up to a conductor bound. As an application we give a lower bound for the corresponding counting problem by discriminant.

Keywords

local function fields abelian galois group g-extensions conductor bound discriminant counting formula

Cite

@article{arxiv.1904.02573,
  title  = {The conductor density of local function fields with abelian Galois group},
  author = {Jürgen Klüners and Raphael Müller},
  journal= {arXiv preprint arXiv:1904.02573},
  year   = {2019}
}

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