We prove in this paper that for $y=x^{\theta}, \frac{11}{20}<\theta\leq\frac{7}{12}$ and $x$ large enough, we have $0.99\frac{y}{\log x}\leq\pi(x)-\pi(x-y)\leq1.01\frac{y}{\log x}$.
Publié le : 1993-07-04
Classification:
Heath-Brown's proof of Huxley's result,
good set,
primes in a short interval,
[MATH]Mathematics [math]
@article{hal-01108692,
author = {Shituo, Lou and Qi, Yao},
title = {The number of primes in a short interval.},
journal = {HAL},
volume = {1993},
number = {0},
year = {1993},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-01108692}
}
Shituo, Lou; Qi, Yao. The number of primes in a short interval.. HAL, Tome 1993 (1993) no. 0, . http://gdmltest.u-ga.fr/item/hal-01108692/