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Zapiski Nauchnykh Seminarov POMI, 2009, Volume 371, Pages 157–170 (Mi znsl3551)  

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
Full-text PDF (609 kB) Citations (6)
References:
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
English version:
Journal of Mathematical Sciences (New York), 2010, Volume 166, Issue 2, Pages 214–221
DOI: https://doi.org/10.1007/s10958-010-9862-8
Bibliographic databases:
Document Type: Article
UDC: 511.466+517.863
Language: Russian
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
Citation in format AMSBIB
\Bibitem{Fom09}
\by O.~M.~Fomenko
\paper On Epstein's zeta function.~II
\inbook Analytical theory of numbers and theory of functions. Part~24
\serial Zap. Nauchn. Sem. POMI
\yr 2009
\vol 371
\pages 157--170
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl3551}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2749231}
\zmath{https://zbmath.org/?q=an:1288.11038}
\elib{https://elibrary.ru/item.asp?id=15321340}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2010
\vol 166
\issue 2
\pages 214--221
\crossref{https://doi.org/10.1007/s10958-010-9862-8}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77952095039}
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  • https://www.mathnet.ru/eng/znsl/v371/p157
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    This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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