The distribution of the multiplicative index of algebraic numbers over residue classes

Pieter Moree, Antonella Perucca, Pietro Sgobba

Let $K$ be a number field and $G$ a finitely generated torsion-free subgroup of $K^{\times }$. Given a prime $\mathfrak{p}$ of $K$ we denote by ${\mathrm{ind}}_{\mathfrak{p}}(G)$ the index o…