A short proof of a Chebotarev density theorem for function fields

TL;DR

This paper presents a simplified proof of a Chebotarev density theorem for function fields over perfect fields with procyclic Galois groups, notably including ramified primes and omitting an error term.

Contribution

It provides a new, streamlined proof of the Chebotarev density theorem in a specific setting, incorporating ramified primes and eliminating the error term.

Findings

Includes ramified primes in the density calculation

Provides a proof without an error term

Simplifies the existing proof of the theorem

Abstract

In this article we discuss a version of the Chebotarev density for function fields over perfect fields with procyclic absolute Galois groups. Our version of this density theorem differs from other versions in two aspects: we include ramified primes and we do not have an error term.