Report
Almost primes of the form $[p^{1/\gamma}]$
| العنوان: | Almost primes of the form $[p^{1/\gamma}]$ |
|---|---|
| المؤلفون: | Xue, Fei, Li, Jinjiang, Zhang, Min |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory |
| الوصف: | 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 $0.989<\gamma<1$, there exist infinitely many primes $p$ such that $[p^{1/\gamma}]=\mathcal{P}_7$, which constitutes an improvement upon the previous result of Banks-Guo-Shparlinski [4] who showed that there exist infinitely many primes $p$ such that $[p^{1/\gamma}]=\mathcal{P}_8$ for $\gamma$ near to one. Comment: 20 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2406.08262 |
| رقم الانضمام: | edsarx.2406.08262 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |