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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


 English version:
Journal of Mathematical Sciences (New York), 2004, 122:6, 3679–3684

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