ULethbridge Number Theory and Combinatorics Seminar: Kelly Emmrich

Let K/k be a finite Galois extension. We define a principal version of the Chebotarev density theorem which represents the density of prime ideals of k that factor into a product of principal prime ideals in K. We find explicit equations to express the principal density in terms of the invariants of K/k and give an effective bound which can be used to verify the non-splitting of the Hilbert exact sequence.