Small gaps between the Piatetski-Shapiro primes
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- by Hongze Li and Hao Pan PDF
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Abstract:
Suppose that $1<c<9/8$. For any $m\geq 1$, there exist infinitely many $n$ such that \begin{equation*} \{[n^c],\ [(n+1)^c],\ \ldots ,\ [(n+k_0)^c]\} \end{equation*} contains at least $m+1$ primes, if $k_0$ is sufficiently large (only depending on $m$ and $c$).References
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Additional Information
- Hongze Li
- Affiliation: School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China
- Email: lihz@sjtu.edu.cn
- Hao Pan
- Affiliation: School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210046, People’s Republic of China
- Email: haopan79@zoho.com
- Received by editor(s): April 15, 2019
- Received by editor(s) in revised form: January 3, 2020
- Published electronically: October 5, 2020
- Additional Notes: This work was supported by the National Natural Science Foundation of China (Grants No. 11671253 and 11671197) and the Specialized Research Fund for the Doctoral Program of Higher Education (No. 20120073110059).
The second author is the corresponding author - © Copyright 2020 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 373 (2020), 8463-8484
- MSC (2010): Primary 11N05; Secondary 11L20, 11N36, 11P32
- DOI: https://doi.org/10.1090/tran/8205
- MathSciNet review: 4177265