Equidistribution of $\alpha p^{\theta }$ with a Chebotarev condition and applications to extremal primes

Amita Malik, Neha Prabhu

We establish a joint distribution result concerning the fractional part of $\alpha p^{\theta }$ for $\theta \in (0,1),\alpha >0$, where $p$ is a prime satisfying a Chebotarev condition in a fixed finite…