• A new approximate functional equation for Hurwitz zeta function for rational parameter

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/107/04/0377-0385

    • Keywords

       

      Hurwitz zeta function; DirichletL-series

    • Abstract

       

      For Hurwitz zeta function ζ(s, (a/k)) witha = 1,2,3,…,k, we obtain a new simple approximate functional equation (uniform ink andt) in critical strip. Our method should prove to be an alternative approach to Atkinson’s method in dealing with$$\sum\nolimits_{x(\bmod q)} {\int_0^T {|L(s,x)|^2 } } dt$$, whereL(s, x) is Dirichlet L-series moduloq and s = σ +it.

    • Author Affiliations

       

      Vivek V Rane1

      1. Department of Mathematics, Institute of Science, 15, Madam Cama Road, Mumbai - 400 032, India
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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