Distribution of Artin-Schreier-Witt extensions

TL;DR

This paper derives precise asymptotic formulas for the distribution of conductors in abelian p-extensions of global function fields, proposing a new conjecture for discriminant distribution supported by a lower bound.

Contribution

It provides exact asymptotic formulas for conductors and introduces a new conjecture on discriminant distribution in the context of Artin-Schreier-Witt extensions.

Findings

Asymptotic formulas for conductors of abelian p-extensions

A new conjecture for discriminant distribution

A lower bound supporting the conjecture

Abstract

The article at hand contains exact asymptotic formulas for the distribution of conductors of abelian p-extensions of global function fields of characteristic p. These yield a new conjecture for the distribution of discriminants fueled by an interesting lower bound.