Date of Award
2016
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Graduate Group
Mathematics
First Advisor
Ted Chinburg
Abstract
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].
Recommended Citation
Sundstrom, James David, "Lower Bounds for Generalized Regulators" (2016). Publicly Accessible Penn Dissertations. 2047.
https://repository.upenn.edu/edissertations/2047