Geodesic
The Selberg $Z$-function and the Lindelöf conjecture
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 16, Tome 269 (2000), pp. 151-163 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is proved that, under some assumptions, the Selberg $Z$-function $Z(s)$ is of order $t^\varepsilon/(\sigma-\frac12)$ in a sufficiently small neighborhood of the critical straight line $\sigma>\frac12$, $t\ge1$, and $\varepsilon>0$ is an arbitrary small but fixed. 
@article{ZNSL_2000_269_a11,
     author = {A. I. Vinogradov},
     title = {The {Selberg} $Z$-function and the {Lindel\"of} conjecture},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {151--163},
     year = {2000},
     volume = {269},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2000_269_a11/}
}
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A. I. Vinogradov. The Selberg $Z$-function and the Lindelöf conjecture. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 16, Tome 269 (2000), pp. 151-163. http://geodesic.mathdoc.fr/item/ZNSL_2000_269_a11/