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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2009 Volume 371, Pages 157–170 (Mi znsl3551)

This article is cited in 6 papers

On Epstein's zeta function. II

O. M. Fomenko

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

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.

UDC: 511.466+517.863

Received: 20.09.2009


 English version:
Journal of Mathematical Sciences (New York), 2010, 166:2, 214–221

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© Steklov Math. Inst. of RAS, 2024