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JOURNALS
// Zapiski Nauchnykh Seminarov POMI
// Archive
Zap. Nauchn. Sem. POMI,
2002
Volume 286,
Pages
169–178
(Mi znsl1575)
This article is cited 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
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
$$ \zeta(1+it;Q)\ll|t|^{1/4+\varepsilon}. $$
UDC:
511.466+517.863
Received:
06.05.2002
Fulltext:
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Cited by
English version:
Journal of Mathematical Sciences (New York), 2004,
122
:6,
3679–3684
Bibliographic databases:
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Steklov Math. Inst. of RAS
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