On Epstein's zeta function. II

O. M. Fomenko

Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 24, Tome 371 (2009), pp. 157-170

Résumé

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.

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