Denisty questions in rings of the form ${\mathcal{O}}_K[\gamma ]\cap K$

Deepesh Singhal, Yuxin Lin

We fix a number field $K$ and study statistical properties of the ring ${\mathcal{O}}_K[\gamma ]\cap K$ as $\gamma$ varies over algebraic numbers of a fixed degree $n\ge 2$. Given $k\ge 1$, w…