Lethbridge Number Theory and Combinatorics Seminar: Peng-Jie Wong

Dirichlet's theorem on arithmetic progressions states that for any (a,q)=1, there are infinitely many primes congruent to a modulo q. Such a theorem together with Euler's earlier work on the infinitude of primes represents the beginning of the study of L-functions and their connection with the distribution of primes.

 

In this talk, we will discuss some ingredients of the proof for the theorem. Also, we will explain how such an L-function approach leads to Dirichlet's theorem for modular forms that gives a count of Fourier coefficients of modular forms over primes in arithmetic progressions.