On the value distribution and moments of the Epstein zeta function to the right of the critical strip

We study the Epstein zeta function $E_n(L,s)$ for $s>\frac{n}{2}$ and determine for fixed $c>\frac{1}{2}$ the value distribution and moments of $E_n(\cdot,cn)$ (suitably normalized) as $n\to\infty$. We further discuss the random function $c\mapsto E_n(\cdot,cn)$ for $c\in[A,B]$ with $\frac{1}{2}<A<B$ and determine its limit distribution as $n\to\infty$.