L-functions and Dirichlet’s Theorem

Mr. Ming-Lun (Eric) Hsieh will give the talk on Friday, March 12 at noon in Math 417. This lecture will be open to all.

Abstract: Dirichlet’s Theorem asserts that there are infinitely many primes in the arithmetic progression a·n + b where a and b are coprime integers, and n ∈ N. It is striking that Dirichlet proved this purely number theoretic result by a totally analytic method. In this talk, I will introduce L-functions, which are meromorphic functions on C, and try to convince you of the validity of Dirichlet’s proof in which he showed that a specific L-function did not vanish at 1. (Everything is taken form Serre's GTM book Course in Arithmetic.)