# An analogue of a formula for Chebotarev Densities

## TL;DR

This paper presents a new formula related to Chebotarev densities for finite Galois extensions, extending Dawsey's work by involving the Riemann zeta function at multiples of s, and shows it as a finite m analogue.

## Contribution

It introduces an analogue of Dawsey's Chebotarev density formula involving the Riemann zeta function for finite Galois extensions, generalizing the limit case.

## Key findings

- Derived a new Chebotarev density formula involving ζ(ms) for m ≥ 2
- Showed the formula reduces to Dawsey's as m approaches infinity
- Extended understanding of Chebotarev densities in relation to zeta functions

## Abstract

In this short note, we show an analogue of Dawsey's formula on Chebotarev densities for finite Galois extensions of $\mathbb{Q}$ with respect to the Riemann zeta function $\zeta(ms)$ for any integer $m\geqslant2$. Her formula may be viewed as the limit version of ours as $m\to\infty$.