Regulator of a number field

Summary

The regulator of an algebraic number field $K$ is a positive real number $R_K$ that measures the size of the unit group. By Dirichlet's unit theorem, the logarithms of the units form a lattice. Up to normalisation, $R_K$ is the volume of a fundamental domain of that lattice. It appears with the class number in the class number formula for the residue of the Dedekind zeta function.