# The principal Chebotarev density theorem

Date: Mon, Feb 13, 2023

Location: Online, PIMS, University of Lethbridge

Conference: Lethbridge Number Theory and Combinatorics Seminar

Subject: Mathematics

Class: Scientific

### Abstract:

**Kelly O'Connor (Colorado State University, USA)**

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.

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