• DirichletL-function and power series for Hurwitz zeta function

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    • Keywords


      Hurwitz zeta function; DirichletL-function; power series

    • Abstract


      For 0 < α < 1, letζ(s, α) be the Hurwitz zeta function and let ζ1 (s, α) = ζ(s, α) -α− s. For a fixeds, we developζ1(s,α) as a power series in α in the complex circle ¦α¦ < 1. If$$\sum\limits_{\chi \left( {\bmod q} \right)} {L\left( {s,\chi } \right)L\left( {s',\bar \chi } \right)} = \frac{{\phi \left( q \right)}}{{q^{s + s'} }}\sum\limits_{k/q} \mu \left( {\frac{q}{k}} \right)\left( {\sum\limits_{a = 1}^k {\left( {\frac{k}{a}} \right)^{\operatorname{Re} s + \operatorname{Re} s'} + Q\left( {s,s',k} \right)} } \right)$$, we obtain an asymptotic expansion for Q(k) =Q(s,s′,k) using the power series forζ1(s,α)

    • Author Affiliations


      V V Rane1

      1. Department of Mathematics, The Institute of Science, 15, Madam Cama Road, Bombay - 400032, India
    • Dates

  • Proceedings – Mathematical Sciences | News

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