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Lecture
Are you an EPFL student looking for a semester project?
Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.
This lecture delves into the concept of primes in arithmetic progression, exploring the relationship between Dirichlet L-functions and characters. The instructor discusses the orthogonality of characters, the analytic continuation of L-functions, and the class number formula. By analyzing the behavior of L-functions at s=1, the lecture aims to demonstrate the divergence of the sum of 1 over p for p congruent to a modulo q. The proof involves showing that the L-function for non-trivial characters tends to infinity as s approaches 1. The lecture also touches upon Legendre symbols and their connection to real characters. Through a detailed analysis, the instructor illustrates the intricate interplay between characters, L-functions, and prime numbers.