An analogue of a formula for Chebotarev Densities

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 $ζ(ms)$ for any integer $m\geqslant2$. Her formula may be viewed as the limit version of ours as $m\to\infty$.

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