Number Theory Seminar

The notion of simultaneous $p$-orderings was introduced by Bhargava in his work on integer-valued polynomials. Let k be a number field and let $O_k$ be its rings of integers. A sequence of elements in $O_k$ is a simultaneous $p$-ordering if it is equidistributed modulo every power of every prime ideal in $O_k$. We show that the only number field for which $O_k$ admits a simultaneous $p$-ordering is $\mathbb{Q}$. It is a joint project with Mikołaj Frączyk.