Malle’s Conjecture for octic $D_4$-fields

Name: Malle’s Conjecture for octic $D_4$-fields
Start: 2020-02-19T15:00:00-05:00
End: 2020-02-19T16:00:00-05:00
Location: Science Center 507

SEMINARS: NUMBER THEORY

When: February 19, 2020

3:00 pm - 4:00 pm

Where: Science Center 507

Address: 1 Oxford Street, Cambridge, MA 02138, United States

Speaker: Ila Varma - University of Toronto

We consider the family of normal octic fields with Galois group $D_4$, ordered by their discriminant. In forthcoming joint work with Arul Shankar, we verify the strong form of Malle’s conjecture for this family of number fields, obtaining the order of growth as well as the constant of proportionality. In this talk, we will discuss and review the combination of techniques from analytic number theory and geometry-of-numbers methods used to prove this and related results.