Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 16, Tome 269 (2000), pp. 151-163
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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/
@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/}
}
TY - JOUR
AU - A. I. Vinogradov
TI - The Selberg $Z$-function and the Lindelöf conjecture
JO - Zapiski Nauchnykh Seminarov POMI
PY - 2000
SP - 151
EP - 163
VL - 269
UR - http://geodesic.mathdoc.fr/item/ZNSL_2000_269_a11/
LA - ru
ID - ZNSL_2000_269_a11
ER -
%0 Journal Article
%A A. I. Vinogradov
%T The Selberg $Z$-function and the Lindelöf conjecture
%J Zapiski Nauchnykh Seminarov POMI
%D 2000
%P 151-163
%V 269
%U http://geodesic.mathdoc.fr/item/ZNSL_2000_269_a11/
%G ru
%F ZNSL_2000_269_a11
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.
