The Chebotarev Density Theorem and its Applications

Specialeforsvar ved Qingyue Zhang 

Titel: The Chebotarev Density Theorem and its Applications

Abstract: This talk will present the Dirichlet-density form of the Chebotarev Density Theorem and its role in describing the distribution of primes in finite Galois extensions. I will begin by introducing the necessary background, including splitting of primes, Frobenius conjugacy classes, and Dirichlet density. I will then outline the main ideas of the analytic proof and briefly compare it with an algebraic proof based on cyclic reduction. Finally, I will discuss several applications, including the determination of Galois closures from splitting primes, factorisation patterns of polynomials modulo primes, and the interpretation of Artin’s primitive root conjecture through Kummer extensions.

Vejleder: Fabien Pazuki