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Zapiski Nauchnykh Seminarov POMI, 2009, Volume 371, Pages 157–170
(Mi znsl3551)
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This article is cited in 6 scientific papers (total 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.
Received: 20.09.2009
Citation:
O. M. Fomenko, “On Epstein's zeta function. II”, Analytical theory of numbers and theory of functions. Part 24, Zap. Nauchn. Sem. POMI, 371, POMI, St. Petersburg, 2009, 157–170; J. Math. Sci. (N. Y.), 166:2 (2010), 214–221
Linking options:
https://www.mathnet.ru/eng/znsl3551 https://www.mathnet.ru/eng/znsl/v371/p157
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Abstract page: | 346 | Full-text PDF : | 88 | References: | 52 |
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