Discrete Limit Theorem for the Epstein Zeta-Function

Abstract

In this paper, the value distribution of the Epstein zeta-function ζ(s; Q) is investigated. It is well known that the asymptotic behaviour of zeta-functions is most effectively defined by probabilistic limit theorems in the sense of weak convergence. A limit theorem of continuous type for the function ζ(s; Q) on the complex plane has been obtained by Laurinčikas and Macaitienė [11]. This paper presents a discrete-type result, based on the Master’s Thesis [8] by Gutauskienė.