Proof of some conjectures on the mean-value of Titchmarsh series - III

Balasubramanian, R. ; Ramachandra, K. (1992) Proof of some conjectures on the mean-value of Titchmarsh series - III Proceedings of the Indian Academy of Sciences - Mathematical Sciences, 102 (2). pp. 83-91. ISSN 0253-4142

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Official URL: http://www.ias.ac.in/j_archive/mathsci/102/2/83-91...

Related URL: http://dx.doi.org/10.1007/BF02836781

Abstract

With some applications in view, the following problem is solved in some special case which is not too special. Let F(s) = ∑n=1 an λn-s be a generalized Dirichlet series with 1 = λ1 < λ2 < ..,λn ≤Dn, and λn+1 - λn ≥ D -1 λn+1 where α>0 and D(≥ 1) are constants. Then subject to analytic continuation and some growth conditions, a lower bound is obtained for (1/H) ∫OH|F(it)|2dt These results will be applied in other papers to appear later.

Item Type:Article
Source:Copyright of this article belongs to Indian Academy of Sciences.
Keywords:Titchmarsh Series; Mean Value; Lower Bounds
ID Code:1345
Deposited On:05 Oct 2010 12:43
Last Modified:16 May 2016 12:29

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