episciences.org_155_1653156460
1653156460
episciences.org
raphael.tournoy+crossrefapi@ccsd.cnrs.fr
episciences.org
HardyRamanujan Journal
28047370
10.46298/journals/hrj
https://hrj.episciences.org
01
01
2006
Volume 29  2006
A remark on a theorem of A. E. Ingham.
K G
Bhat
K
Ramachandra
Referring to a theorem of A. E. Ingham, that for all $N\geq N_0$ (an absolute constant), the inequality $N^3\leq p\leq(N+1)^3$ is solvable in a prime $p$, we point out in this paper that it is implicit that he has actually proved that $\pi(x+h)\pi(x) \sim h(\log x)^{1}$ where $h=x^c$ and $c (>\frac{5}{8})$ is any constant. Further, we point out that even this stronger form can be proved without using the functional equation of $\zeta(s)$.
01
01
2006
155
https://hal.archivesouvertes.fr/hal01111487v1
10.46298/hrj.2006.155
https://hrj.episciences.org/155

https://hrj.episciences.org/155/pdf