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

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/102/02/0083-0091

• # Keywords

Titchmarsh series; mean value; lower bounds

• # Abstract

With some applications in view, the following problem is solved in some special case which is not too special. LetF(s) =Σn=1anλn−s be a generalized Dirichlet series with 1 =λ1 &lt;λ2 &lt; …,λnDn, andλn+1 -λnD− 1λn+1− a where α&gt;0 andD(≥ 1) are constants. Then subject to analytic continuation and some growth conditions, a lower bound is obtained for$$(1/H)\int {_O^H |} F(it)|^2 dt$$. These results will be applied in other papers to appear later.

• # Author Affiliations

1. The Institute of Mathematical Sciences, Madras - 600113, India
2. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay - 400005, India

• # Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 5
November 2019

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