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. 
@article{IM2_2008_72_3_a1,
     author = {M. A. Korolev},
     title = {On the integral of {Hardy's} function $Z(t)$},
     journal = {Izvestiya. Mathematics },
     pages = {429--478},
     publisher = {mathdoc},
     volume = {72},
     number = {3},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2008_72_3_a1/}
}
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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/