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      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 <λ2 < …,λnDn, andλn+1 -λnD− 1λn+1− a where α>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

       

      R Balasubramanian1 K Ramachandra1 2

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

       
  • Proceedings – Mathematical Sciences | News

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