Abstract:
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.
Key words and phrases:Epstein's zeta function, functional equation, zeros of Epstein's zeta function.