Scientific Calendar Event

A vector of the space of integers $\Z^n$ $(n>1)$ is called divisible if it is the product of some other vector of this space by an integer greater than 1.

The uniform distribution of a set $M$ in the $n$-dimensional integer space means that for any domain the number of points of $M$ in this domain, dilated homothetically with homothety coefficient $N$ is asymptotically proportional to the volume of this domain, multiplied by $N^n$. The proportionality coefficient is called the density of $M$.

THEOREM.  The set $M$ of the nondivisible vectors of $\Z^n$ (n>1) is distributed there uniformly with density $1/\zeta(n)$, where $\zeta$ is the Euler zeta function.

Example.  The density of the set of nondivisible vectors in the plane lattice equals $1/\zeta(2)=6/\pi^2\approx 2/3$.
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