Geodesic
On the integral of Hardy's function $Z(t)$
Izvestiya. Mathematics , Tome 72 (2008) no. 3, pp. 429-478.

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We prove asymptotic formulae for the values of the integral of Hardy's function $Z(t)$ at special points and obtain an omega-theorem and an upper bound for the integral of $Z(t)$ that are sharp with respect to the rate of growth. 
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M. A. Korolev. On the integral of Hardy's function $Z(t)$. Izvestiya. Mathematics , Tome 72 (2008) no. 3, pp. 429-478. http://geodesic.mathdoc.fr/item/IM2_2008_72_3_a1/

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