Some Upper Bounds on Dense Module Sublattices from Number Fields

par Frédérique Oggier

mardi 10 nov. 2026, 14:30 → 16:00 Europe/Paris

Salle de conférences (XLIM)

We consider the problem of finding dense rank one module sublattices in module lattices of a given rank, where by module lattice we mean a lattice obtained as $R$-linear combinations of vectors with coefficients in a number field $K$, with ring of integers $\mathcal{O}_K$, and $R\subseteq \mathcal{O}_K$ an order. We provide generic upper bounds on the normalized volume of rank one module sublattices for $K$ totally real or CM, specific bounds for quadratic extensions and some cyclotomic extensions, as well as exact values for some norm Euclidean quadratic extensions.