On Cesàro Theorem for Number Fields

Andrea Ferraguti, Giacomo Micheli

Published 2014-09-23Version 1

Let $K$ be a number field of degree $n$ and let $m\geq n$. We show that the density of the set of coprime $m$-tuples of algebraic integers is ${1/\zeta_K(m)}$, where $\zeta_K$ is the Dedekind zeta function of $K$. This generalizes a result by Ces\`aro (1881) concerning the density of coprime pairs in $\mathbb{Z}$.