Average of $3$-torsion in class groups of $2$-extensions

Abstract: In 1971, Davenport and Heilbronn proved 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 extensions. This is a joint work with Robert J. Lemke Oliver and Melanie Matchett Wood.

number theory

Audience: researchers in the topic

( slides )

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MIT number theory seminar

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