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Zapiski Nauchnykh Seminarov POMI, 2002, Volume 286, Pages 169–178 (Mi znsl1575)  
This article is cited in 5 scientific papers (total in 5 papers)

On Epstein's zeta-function

O. M. Fomenko

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
Full-text PDF (190 kB) Citations (5)
Abstract: Let $Q(x_1,x_2,x_3)=x^2_1+x^2_2+x^2_3$, and let $\zeta(s;Q)$ be Epstein's zeta-function of the form $Q$. It is proved that for $|t|>C>0$ one has the estimate
$$ \zeta(1+it;Q)\ll|t|^{1/4+\varepsilon}. $$
Received: 06.05.2002
English version:
Journal of Mathematical Sciences (New York), 2004, Volume 122, Issue 6, Pages 3679–3684
DOI: https://doi.org/10.1023/B:JOTH.0000035244.03387.7d
Bibliographic databases:
UDC: 511.466+517.863
Language: Russian
Citation: O. M. Fomenko, “On Epstein's zeta-function”, Analytical theory of numbers and theory of functions. Part 18, Zap. Nauchn. Sem. POMI, 286, POMI, St. Petersburg, 2002, 169–178; J. Math. Sci. (N. Y.), 122:6 (2004), 3679–3684
Citation in format AMSBIB
\Bibitem{Fom02}
\by O.~M.~Fomenko
\paper On Epstein's zeta-function
\inbook Analytical theory of numbers and theory of functions. Part~18
\serial Zap. Nauchn. Sem. POMI
\yr 2002
\vol 286
\pages 169--178
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1575}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1937376}
\zmath{https://zbmath.org/?q=an:02183320}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2004
\vol 122
\issue 6
\pages 3679--3684
\crossref{https://doi.org/10.1023/B:JOTH.0000035244.03387.7d}
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  • https://www.mathnet.ru/eng/znsl/v286/p169
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    This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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