• On the mean square value of Hurwitz zeta function

• # Fulltext

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 &lt;a &lt; 1.

• # Author Affiliations

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

• # Proceedings – Mathematical Sciences

Volume 130, 2020
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019