HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information

A Chebychev's type of prime number theorem in a short interval II.

Abstract : In this paper, we show that $0.969\frac{y}{\log x}\leq\pi(x)-\pi(x-y)\leq1.031\frac{y}{\log x}$, where $y=x^{\theta}, \frac{6}{11}<\theta\leq 1$ with $x$ large enough. In particular, it follows that $p_{n+1}-p_n<\!\!\!0$, where $p_n$ denotes the $n$th prime.
Keywords :
Document type :
Journal articles
Domain :

Cited literature [5 references]

https://hal.archives-ouvertes.fr/hal-01108637
Contributor : Ariane Rolland Connect in order to contact the contributor
Submitted on : Friday, January 23, 2015 - 11:05:38 AM
Last modification on : Monday, March 28, 2022 - 8:14:08 AM
Long-term archiving on: : Friday, April 24, 2015 - 10:16:46 AM

File

15Article1.pdf
Explicit agreement for this submission

Citation

Lou Shituo, Yao Qi. A Chebychev's type of prime number theorem in a short interval II.. Hardy-Ramanujan Journal, Hardy-Ramanujan Society, 1992, Volume 15 - 1992, pp.1 - 33. ⟨10.46298/hrj.1992.124⟩. ⟨hal-01108637⟩

Record views