Year: 2026
Type: preprint
Abstract: Denote by $Π_γ(x)$ the number of primes $p \leqslant x$ such that $[p^{1/γ}]$ is also a prime. In this paper, it is proved that the expected asymptotic formula \begin{equation*} Π_γ(x)=\frac{γx}{(\log x)^2} (1+o(1)) \end{equation*} holds for $γ> 15/13$, which constitutes an improvement upon the previous result of Balog [2] who showed that the above asymptotic formula holds for $γ> 6/5$.
Source: arXiv (Cornell University)
Authors: Long, Linji, Li, Jinjiang, Zhang, Min
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G2900710960, G382562614, G55069091, G6461339978
OpenAlex ID: W7221833191