Community Connections Events for Students

Save the date for Harvey Mudd and Caltech’s virtual career fair! Registration will open in January for students and alumni to participate in the event. Connect with employers actively hiring for internships and full-time roles!

“Dirichlet’s Theorem and the Rise of Analytic Number Theory”

Abstract

In 1837, Peter Dirichlet proved the following theorem: If a and d are relatively prime integers, then the arithmetic progression a, a+d, a+2d, . . . contains infinitely many prime numbers. His proof ushered in a revolution in number theory because it relied in a critical way on complex analysis. The use of analytic methods to solve problems in number theory was a tremendous innovation at the time. We shall consider some of the details of Dirichlet’s proof, focusing on understanding why there is a deep connection between these seemingly unrelated branches of mathematics. Throughout, we will be more concerned with the ideas underlying the proof than we will with presenting an excessive amount of technical detail.