English

On almost primes in Piatetski-Shapiro sequences

Number Theory 2025-05-16 v1

Abstract

The author proves that for 0.9985<γ<10.9985 < \gamma < 1, there exist infinitely many primes pp such that [p1/γ][p^{1/\gamma}] has at most 5 prime factors counted with multiplicity. This gives an improvement upon the previous results of Banks-Guo-Shparlinski and Xue-Li-Zhang.

Keywords

Cite

@article{arxiv.2505.09634,
  title  = {On almost primes in Piatetski-Shapiro sequences},
  author = {Runbo Li},
  journal= {arXiv preprint arXiv:2505.09634},
  year   = {2025}
}

Comments

8 pages

R2 v1 2026-06-28T23:33:28.071Z