• On the mean square value of Hurwitz zeta function

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      https://www.ias.ac.in/article/fulltext/pmsc/090/03/0195-0212

    • Keywords

       

      Hybrid analogue for L-series; Balasubramanian’s theorem

    • Abstract

       

      R Balasubramanian has shown that$$\mathop \smallint \limits_1^{\rm T} |\zeta (\tfrac{1}{2} + it)|^2 dt = T\log \tfrac{T}{{2\pi }} + (2\gamma - 1)T + O(T^{\theta + \in } )$$ with θ = 1/3. In this paper we develop a hybrid analogue for the mean square value of the Hurwitz zeta function ζ (s, a) and show that (i) new asymptotic terms arise in the expression for ζ (s, a) which are not present in the above expression for the ordinary zeta function and (ii) the corresponding error term is given by$$O(T^{5/12} log^2 T) + O\left( {\frac{{logT}}{{\left\| {2a} \right\|}}} \right)$$ for 0 <a < 1.

    • Author Affiliations

       

      M J Narlikar1

      1. 701, Colaba Housing Colony, Homi Bhabha Road, Bombay - 400 005, India
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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