On the frequency of Titchmarsh's phenomenon for ζ(s)-III

Balasubramanian, R. ; Ramachandra, K. (1977) On the frequency of Titchmarsh's phenomenon for ζ(s)-III Proceedings of the Indian Academy of Sciences, Section A, 86 (4). pp. 341-351. ISSN 0370-0089

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Official URL: http://www.ias.ac.in/j_archive/proca/86/4/341-351/...

Related URL: http://dx.doi.org/10.1007/BF03046849

Abstract

We obtain a lower bound for max |ιζ(½+it)| as t varies overT < t < T+Y, where (log T)1/100 < Y < T, as a function of Y(1/100 is unimportant). Our lower bound is exp {D(log Y)½ (log log Y)−½} where D is a positive constant. (After submitting this paper for publication we came to know through a preprint of H L Montgomery that he had proved our result in the case Y=T. In his proof an essential assumption is Riemann hypothesis and our result is independent of any such unproved hypothesis. However he has other new results which are free from any hypothesis).

Item Type:Article
Source:Copyright of this article belongs to Indian Academy of Sciences.
Keywords:Riemann Zeta-function; Titchmarsh's Phenomenon; Ω-Theorems
ID Code:49191
Deposited On:19 Jul 2011 09:43
Last Modified:18 May 2016 04:00

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