A Remark on a theory of A.E. Ingham

Ramachandra, K and Bhat, Kishor G (2006) A Remark on a theory of A.E. Ingham. Hardy Ramanujan Journal, 29. pp. 37-43.

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Abstract: Referring to a theorem of A. E. Ingham, that for all N≥N0 (an absolute constant), the inequality N3≤p≤(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 π(x+h)−π(x)∼h(logx)−1 where h=xc and c(>58) is any constant. Further, we point out that even this stronger form can be proved without using the functional equation of ζ(s).
Item Type: Article
Subjects: School of Natural and Engineering Sciences > Mathematics
Doctoral Programme > PhD Scholar Publications
Date Deposited: 22 Apr 2021 17:17
Last Modified: 29 Apr 2021 16:53
Official URL: https://hrj.episciences.org/155/pdf
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    Funders: UNSPECIFIED
    Projects: UNSPECIFIED
    DOI:
    URI: http://eprints.nias.res.in/id/eprint/2086

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