On the mean square of the Epstein zeta-function

• Date: 2018
• Main Authors: Savastru, O. V., Varbanets, P. D.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: Epstein zeta-function; approximate functional equation; asymptotic formula; second power moment; 11N37; 11R42
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/920
• Journal Title: Algebra and Discrete Mathematics

We consider the second power moment of the Epstein zeta-function and construct the asymptotic formula in special case, when \(\varphi_{0}(u,v)=u^{2}+Av^{2}\), \(A>0\), \(A\equiv1,2(mod\,4)\) and \(\varphi_{0}(u,v)\) belongs to the one-class kind \(G_{0}\) of the quadratic forms of discriminan...