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An asymptotic formula for the primitive of Hardy’s function

Matti Jutila Department of Mathematics, University of Turku

Number Theory mathscidoc: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 $\frac{3}{4}$ .
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@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.
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