Anders Södergren
On the value distribution and moments of the Epstein zeta function to the right of the critical strip.
Чт, 06/10/2010 - 15:01 — SomNambulAuthors: Anders Södergren
Subjects: Number Theory
AbstractWe 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 $n\to\infty$.On the Poisson distribution of lengths of lattice vectors in a random lattice.
Чт, 01/21/2010 - 16:01 — SomNambulAuthors: Anders Södergren
Subjects: Number Theory
AbstractWe prove that the volumes determined by the lengths of the non-zero vectors
$\pm\vecx$ in a random lattice L of covolume 1 define a stochastic process
that, as the dimension n tends to infinity, converges weakly to a Poisson
process on the positive real line with intensity 1/2. This generalizes earlier
results by Rogers and Schmidt.
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