Lin Jie (Jussieu)
On the Ramanujan conjecture for cuspidal representations of GL_n, after Clozel

Abstract: The original Ramanujan conjecture predicts a boundary for the Fourier coefficients of modular forms. Its generalization to automorphic representations says that the local component of a cuspidal representation of GL_n is tempered. L. Clozel has proved this conjecture for the unramified components of a cuspidal, auto-dual and cohomological representation of GL_n over a CM or totally real field. In the talk, we will first introduce the theory of base change for automorphic representations and then we show Clozel's proof.