Szego Seminar: Dirichlet’s Theorem: A Gem from Classical Number Theory

Abstract: Among early proofs of the infinitude of primes, the one that arose from Euler’s study of the zeta function’s behavior at one remains engaging. The natural next step is the study of primes arising in arithmetic progressions. The infinitude of such sets is Dirichlet’s theorem and the aim of this talk. We will follow Serre’s presentation and generalize Euler’s insight; along the way, we will learn about characters, Euler products, L-series, and other concepts. Time permitting, we will see applications of the theorem, including in a recent paper on “The density of elliptic Dedekind sums” (N.B., J. Branch, R. Heikkinen, C. Nunn, T-A. Wong).