Almost primes of the form $[p^{1/γ}]$
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914833047224320 |
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| author | Xue, Fei Li, Jinjiang Zhang, Min |
| author_facet | Xue, Fei Li, Jinjiang Zhang, Min |
| contents | Let $\mathcal{P}_r$ denote an almost-prime with at most $r$ prime factors, counted according to multiplicity. In this paper, it is proved that, for $0.989<γ<1$, there exist infinitely many primes $p$ such that $[p^{1/γ}]=\mathcal{P}_7$, which constitutes an improvement upon the previous result of Banks-Guo-Shparlinski [4] who showed that there exist infinitely many primes $p$ such that $[p^{1/γ}]=\mathcal{P}_8$ for $γ$ near to one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_08262 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Almost primes of the form $[p^{1/γ}]$ Xue, Fei Li, Jinjiang Zhang, Min Number Theory Let $\mathcal{P}_r$ denote an almost-prime with at most $r$ prime factors, counted according to multiplicity. In this paper, it is proved that, for $0.989<γ<1$, there exist infinitely many primes $p$ such that $[p^{1/γ}]=\mathcal{P}_7$, which constitutes an improvement upon the previous result of Banks-Guo-Shparlinski [4] who showed that there exist infinitely many primes $p$ such that $[p^{1/γ}]=\mathcal{P}_8$ for $γ$ near to one. |
| title | Almost primes of the form $[p^{1/γ}]$ |
| topic | Number Theory |
| url | https://arxiv.org/abs/2406.08262 |