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Galois Seminar

Friday, April 24, 2015 - 3:15pm

James Sundstrom

University of Pennsylvania

Location

University of Pennsylvania

DRL 4N30

If L/K is an extension of number fields, let E_L denote the units of L and let E_{L/K} denote the relative units of L/K. Similar to how the regulator Reg(L) is defined using the full unit group E_L, the relative regulator Reg(L/K) can be defined using E_{L/K}. In the same way, one can define generalized regulators associated to other subgroups E of the units of L. For each subgroup E, there is also a corresponding theta series. Friedman and Skoruppa demonstrated how the theta series associated to E_{L/K} can be used to find a lower bound for Reg(L/K). I will discuss how their method can be applied to other subgroups E to obtain lower bounds for other generalized regulators.