In 1999, Friedman and Skoruppa demonstrated a method to derive lower bounds for the relative regulator of an extension L/K of number fields. The relative regulator is defined using the subgroup of relative units of L/K. It appears in the theta series associated to this subgroup, so an inequality relating the theta series and its derivative provides an inequality for the relative regulator. This same technique can be applied to other subgroups E of the units of a number field $L$. In this thesis, we consider the case where E is the intersection of two subgroups of relative units to real quadratic fields; the corresponding regulator grows exponentially in [L:Q].