Dirichlet’s Theorem on Arithmetic Progressions

24.10.2024 17:30 – 18:30

In 1837, Dirichlet proved that every arithmetic progression where the first term and the common difference are coprime contains infinitely many primes. This result, known as Dirichlet’s Theorem on Arithmetic Progressions, is a foundational milestone in analytic number theory, a field that Dirichlet's proof helped inaugurate, building on earlier contributions from Euler and others.

In this talk, we will outline Dirichlet's original argument with a modern perspective. Before delving into the proof, we will review harmonic analysis on finite abelian groups and introduce key aspects of Dirichlet series. The aim of this talk is threefold: to showcase the elegance of Dirichlet’s approach, to present the material in a way accessible to master’s students, and to lay the groundwork or at least a motivation for a potential follow-up talk on the Prime Number Theorem for arithmetic progressions.

Lieu

Bâtiment: Conseil Général 7-9

Room 6-13

entrée libre