On the mean square of the Epstein zeta-function

• Published in: Algebra and Discrete Mathematics
• Date: 2005
• Main Authors: Savastru, O.V., Varbanets, P.D.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2005
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/156605
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: On the mean square of the Epstein zeta-function / O.V. Savastru, P.D. Varbanets // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 1. — С. 105–121. — Бібліогр.: 16 назв. — англ.

We consider the second power moment of the Epstein zeta-function and construct the asymptotic formula in special
 case, when ϕ₀(u,v) = u² + Av² , A > 0, A ≡ 1, 2(mod 4) and
 ϕ0(u,v) belongs to the one-class kind G₀ of the quadratic forms of
 discriminant −4A....