# MathSciDoc: An Archive for Mathematician ∫

#### Number Theorymathscidoc:1701.24007

Arkiv for Matematik, 49, (1), 97-107, 2009.3
Let$Z$($t$) be the classical Hardy function in the theory of Riemann’s zeta-function. An asymptotic formula with an error term$O$($T$^{1/6}log$T$) is given for the integral of$Z$($t$) over the interval [0,$T$], with special attention paid to the critical cases when the fractional part of $\sqrt{T/2\pi }$ is close to $\frac{1}{4}$ or $\frac{3}{4}$ .
@inproceedings{matti2009an,
title={An asymptotic formula for the primitive of Hardy’s function},
author={Matti Jutila},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203629477755995},
booktitle={Arkiv for Matematik},
volume={49},
number={1},
pages={97-107},
year={2009},
}

Matti Jutila. An asymptotic formula for the primitive of Hardy’s function. 2009. Vol. 49. In Arkiv for Matematik. pp.97-107. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203629477755995.