Simultaneous $\mathfrak{p}$-orderings and equidistribution

Abstract

Let $D$ be a Dedekind domain. Roughly speaking, a simultaneous $\mathfrak{p}$-ordering is a sequence of elements from $D$ which is equidistributed modulo every power of every prime ideal in $D$ as well as possible. Bhargava asked which subsets of the Dedekind domains admit simultaneous $\mathfrak{p}$-orderings. We give an overview on the progress in this problem. We also explain how it relates to the theory of integer valued polynomials and list some open problems.