6 problems

Let $N_n(X)$ denote the number of isomorphism classes of monogenic number fields $K$ of degree $n$ with $|D_K|\leq X$ and associated Galois group $S_n$. Bhargava–Shankar–Wang order…

Let $0\ne m\in\mathbb Z$ be a rational integer satisfying ()—that is, $m\ne 1$ is square-free and $m\not\equiv 1\pmod 4$—with $m<0$. Set $K=\mathbb Q(\sqrt[8]{m})$ and identify gen…

Non-monogenicity conjecture. Most number fields of degree greater than $2$ are not monogenic.

Let $K$ be the composite number field considered in the paper, with integer parameter $m$. The preceding corollary shows that $K$ is not monogenic when $|m|\not=2,3,5,6,10,15,30$.…

Let $m\in\{\pm3,\pm5,\pm15,\pm17\}$. The fields $\mathbb{Q}(i,\sqrt[4]{m})$ are octic fields; the cases $m=\pm1$ are excluded because they do not give octic fields. Non-monogenity…

Let $f$ be an irreducible polynomial of fixed degree at least $4$ with randomly chosen coefficients, and let $K$ be the number field obtained by adjoining a root of $f$ to…