K G Bhat ; K Ramachandra - A remark on a theorem of A. E. Ingham.

hrj:155 - Hardy-Ramanujan Journal, January 1, 2006, Volume 29 - 2006 - https://doi.org/10.46298/hrj.2006.155
A remark on a theorem of A. E. Ingham.Article

Authors: K G Bhat 1; K Ramachandra 2

Referring to a theorem of A. E. Ingham, that for all NN0 (an absolute constant), the inequality N3p(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).


Volume: Volume 29 - 2006
Published on: January 1, 2006
Imported on: March 3, 2015
Keywords: Analytic Number Theory,Riemann Zeta-function,Hardy,Hurwitz Zeta-function,Weyl,Littlewood,[MATH]Mathematics [math]

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