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). |
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| Item Type: | Journal Paper |
| 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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