Equidistribution in number fields

Abstract: The notion of $\mathfrak{p}$-ordering comes from the work of Bhargava on integer-valued polynomials. Let $k$ be a number field and let $\mathcal{O}_{k}$ be its ring of integers. A sequence of elements in $\mathcal{O}_{k}$ is a simultaneous $\mathfrak{p}$-ordering if it is equidistributed modulo every prime ideal in $\mathcal{O}_{k}$ as well as possible. We prove that $\mathbb{Q}$ the only number field $k$ such that $\mathcal{O}_{k}$ admits a simultaneous $\mathfrak{p}$-ordering. It is a joint work with Mikołaj Frączyk.

number theory

Audience: researchers in the topic

Warsaw Number Theory Seminar