English

On primes in special sequences with applications to Carmichael numbers

Number Theory 2025-02-11 v2

Abstract

By involving some exponential sums related to Λ(n)\Lambda(n) in arithmetic progression, we can obtain some new results for von Mangoldt function over {\bf nonhomogeneous} Beatty sequences in arithmetic progressions, which improve some recent results of Banks-Yeager unconditionally. On the other hand, we also considered the primes over Piatetski-Shapiro sequences in arithmetic progressions, which gives a continuous improvement of the results of \cite{BBB}. These results can be used to improve some results related to the Carmichael numbers.

Keywords

Cite

@article{arxiv.2207.02378,
  title  = {On primes in special sequences with applications to Carmichael numbers},
  author = {Wei Zhang},
  journal= {arXiv preprint arXiv:2207.02378},
  year   = {2025}
}