On almost primes in Piatetski-Shapiro sequences

Runbo Li

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arXiv · 2505.09634

On almost primes in Piatetski-Shapiro sequences

Runbo Li

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Abstract

The author proves that for $0.9985 < \gamma < 1$, there exist infinitely many primes $p$ such that $[p^{1/\gamma}]$ 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.

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Runbo Li. 2025-05-04. On almost primes in Piatetski-Shapiro sequences. https://arxiv.org/abs/2505.09634

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