This book is an introduction to the multiplicative theory of prime numbers. It is divided roughly into two parts. The first part introduces the classical methods based on analytic properties of Dirichlet series, leading to the fundamental results about the prime number theory in arithmetic progressions. The second part presents methods in the forefront of current research to prove a theorem of Duke, Friedlander and Iwaniec on equidistribution of roots of a quadratic polynomial modulo primes. This result is discussed throughout the book. The two main points are a sieve result not restricted to "almost primes", and the use of results coming from the spectral theory of automorphic forms.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

Readership

Graduate students and research mathematicians interested in number theory.

Table of Contents

• Introduction
• Préparatifs pour le théorème des nombres premiers
• Le théorème des nombres premiers
• Discussion du théorème des nombres premiers
• Crible et sommes oscillantes sur les nombres premiers
• Formes automorphes et décomposition spectrale
• Estimation d'une série de Poincaré
• Équirépartition des racines de congruences quadratiques et applications
• Examen--Bordeaux, Mai 2002
• Bibliographie
• Index