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

Anders Södergren

paper

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

arXiv:1006.1723

Abstract

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 $E_{n} (\cdot, c n)$ (suitably normalized) as $n \to \infty$ . We further discuss the random function $c \mapsto E_{n} (\cdot, c n)$ for $c \in [A, B]$ with $\frac{1}{2} < A < B$ and determine its limit distribution as $n \to \infty$ .

arXiv comment30 pages; revised statement of Proposition 2.1