The University of Arizona
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Average of $3$-torsion in class groups of $2$-extensions

Algebra and Number Theory Seminar

Average of $3$-torsion in class groups of $2$-extensions
Series: Algebra and Number Theory Seminar
Location: ONLINE
Presenter: Jiuya Wang, Duke Univ.

In 1971, Davenport and Heilbronn prove the celebrated theorem
determining the average of $3$-torsion in class groups of quadratic
extensions. In this talk, we will study the average of $3$-torsion in
class groups of $2$-extensions, which are towers of relative quadratic
extensions. As an example, we determine the average of $3$-torsion in
class groups of $D_4$ quartic extension. This is a joint work with
Robert J. Lemke Oliver and Melanie Matchett Wood.