This book consists of lecture notes given by the author at the University of Bordeaux in 2001/2002. It aims to give an introduction into analytic number theory with an emphasis on multiplicative structures. Its main theme is centered on the theorem of prime numbers in arithmetic progression. All standard notions and results about Dirichlet and Poincare series, L-functions, Riemannian geometry and automorphic forms are reviewed in the text. The only exception is the fifth chapter on sieves in number theory, containing a recent result of Duke-Friedlander-Iwaniec on oscillating sieves. The lecture series is written in French.

Reviewer:

pso