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

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

2010-06-09

arxiv.org/abs/1006.1723v2

Journal of Number Theory 131 (2011) 1176-1208

Mathematics

Number Theory

30 pages; revised statement of Proposition 2.1

Scientific paper

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}and determine its limit distribution as $n\to\infty$.

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