The Bombieri-Vinogradov theorem for nilsequences

@article{Shao2020TheBT,
  title={The Bombieri-Vinogradov theorem for nilsequences},
  author={Xuancheng Shao and Joni Teravainen},
  journal={arXiv: Number Theory},
  year={2020}
}
We establish results of Bombieri-Vinogradov type for the von Mangoldt function $\Lambda(n)$ twisted by a nilsequence. In particular, we obtain Bombieri-Vinogradov type results for the von Mangoldt function twisted by any polynomial phase $e(P(n))$; the results obtained are as strong as the ones previously known in the case of linear exponential twists. We derive a number of applications of these results. Firstly, we show that the primes $p$ obeying a "nil-Bohr set" condition, such as $\|\alpha… 

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