Number Fields with Arbitrarily Large Minimal Index

Abstract

For a number field $K/\mathbb{Q}$, the minimal index is the least positive integer $m$ for which there exists a monogenic order with index $m$ in the maximal order. For any $n>2$ and $N>1$, we construct infinitely many number fields of degree $n$ with minimal index greater than $N$.

6 pages, comments welcome!