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.

14 pages, survey, to appear in conference proceedings "Algebras and Polynomials: Algebraic, Number Theoretic, and Topological Aspects of Ring Theory"