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arXiv · 0907.3803

On the integral of Hardy's function

Aleksandar Ivić
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Abstract

If $Z(t) = χ^{-1/2}(1/2+it)ζ(1/2+it)$ denotes Hardy's function, where $ζ(s) = χ(s)ζ(1-s)$ is the functional equation of the Riemann zeta-function, then it is proved that $$ \int_0^T Z(t)\d t = O_\e(T^{1/4+\e}). $$

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Aleksandar Ivić. 2009-07-22. On the integral of Hardy's function. https://arxiv.org/abs/0907.3803

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