Geodesic
Hardy's function $Z(t)$: Results and problems
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic and combinatorial number theory, Tome 296 (2017), pp. 111-122

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This is primarily an overview article on some results and problems involving the classical Hardy function $Z(t) := \zeta (1/2+it)(\chi (1/2+it))^{-1/2}$, $\zeta (s) = \chi (s)\zeta (1-s)$. In particular, we discuss the first and third moments of $Z(t)$ (with and without shifts) and the distribution of its positive and negative values. A new result involving the distribution of its values is presented. 
@article{TM_2017_296_a7,
     author = {A. Ivi\'c},
     title = {Hardy's function $Z(t)$: {Results} and problems},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {111--122},
     publisher = {mathdoc},
     volume = {296},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2017_296_a7/}
}
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A. Ivić. Hardy's function $Z(t)$: Results and problems. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic and combinatorial number theory, Tome 296 (2017), pp. 111-122. http://geodesic.mathdoc.fr/item/TM_2017_296_a7/