On Epstein's zeta function.~II
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 24, Tome 371 (2009), pp. 157-170
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Let $\zeta_3(s)$ be the Epstein zeta function associated with $x^2_1+x^2_2+x^2_3$. We investigate the behavior as $T\to\infty$ of the mean values
$$
\int^T_1|\zeta_3(1+it)|^2\,dt\quad\text{and}\quad\int^T_1|\zeta_3(\sigma+it)|^2\,dt,
$$
$\sigma>1$. Also we discuss the hypothetical distribution of the zeros of $\zeta_3(s)$ in the strip $0\le\sigma\le3/2$. Bibl. – 20 titles.
@article{ZNSL_2009_371_a11,
author = {O. M. Fomenko},
title = {On {Epstein's} zeta {function.~II}},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {157--170},
publisher = {mathdoc},
volume = {371},
year = {2009},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2009_371_a11/}
}
O. M. Fomenko. On Epstein's zeta function.~II. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 24, Tome 371 (2009), pp. 157-170. http://geodesic.mathdoc.fr/item/ZNSL_2009_371_a11/