The number of primes in a short interval.

Lou Shituo (1) , Yao Qi (1)

1 Dalhousie University [Halifax]

We prove in this paper that for $y=x^{\theta}, \frac{11}{20}<\theta\leq\frac{7}{12}$ and $x$ large enough, we have $0.99\frac{y}{\log x}\leq\pi(x)-\pi(x-y)\leq1.01\frac{y}{\log x}$.

Mots clés: primes in a short interval; Heath-Brown's proof of Huxley's result; good set

Domaines: Mathématiques [math]

Lou Shituo, Yao Qi. The number of primes in a short interval.. Hardy-Ramanujan Journal, 1993, Volume 16 - 1993, pp.21-43. ⟨10.46298/hrj.1993.127⟩. ⟨hal-01108692⟩