# Christopher Frei: Quantitative results about norms in abelian extensions

**Time: **
Wed 2019-10-30 10.00 - 11.00

**Location: **
306, SU

**Lecturer: **
Christopher Frei, University of Manchester

### Abstract

We will discuss ways of counting \(G\)-extensions of a given number field, where \(G\) is an abelian group. This is applied to obtain quantitative results about extensions that satisfy the Hasse norm principle, and about extensions realising given elements of the base field as norms. The discussed results are joint work with Dan Loughran and Rachel Newton, and with Rodolphe Richard.