2:15 pm, Lecture Hall 3 On the generalized BrauerSiegel Theorem Anup Dixit University of Toronto. 220517 Abstract For a number field K over Q, there is an associated invariant called the class number, which captures how far the ring of integers of K, is from being a principal ideal domain (PID). The study of class numbers is an important theme in algebraic number theory. In order to understand how the class number varies on varying the number field, Siegel showed that the class number times the regulator approaches infinity for a sequence of quadratic number fields. Later, Brauer extended this to a sequence of Galois extensions over Q, with some additional hypothesis. This is called the famous BrauerSiegel Theorem. Recently, Tsfasman and Vladut conjectured a generalized BrauerSiegel statement for sequence of number fields. In this talk, we prove the classical BrauerSiegel and the generalized version in several unknown cases.
