10.46298/hrj.2006.155
https://hrj.episciences.org/155
Bhat, K G
K G
Bhat
Ramachandra, K
K
Ramachandra
A remark on a theorem of A. E. Ingham.
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 $\zeta(s)$.
episciences.org
Littlewood
Weyl
Hurwitz Zeta-function
Hardy
Riemann Zeta-function
Analytic Number Theory
[MATH] Mathematics [math]
2015-06-12
2006-01-01
2006-01-01
en
journal article
https://hal.archives-ouvertes.fr/hal-01111487v1
2804-7370
https://hrj.episciences.org/155/pdf
VoR
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Hardy-Ramanujan Journal
Volume 29 - 2006
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