This book provides a self contained, thorough introduction to the analytic and probabilistic methods of number theory. The prerequisites being reduced to classical contents of undergraduate courses, it offers to students and young researchers a systematic and consistent account on the subject. It is also a convenient tool for professional mathematicians, who may use it for basic references concerning many fundamental topics.
Deliberately placing the methods before the results, the book will be of use beyond the particular material addressed directly. Each chapter is complemented with bibliographic notes, useful for descriptions of alternative viewpoints, and detailed exercises, often leading to research problems.
This third edition of a text that has become classical offers a renewed and considerably enhanced content, being expanded by more than 50 percent. Important new developments are included, along with original points of view on many essential branches of arithmetic and an accurate perspective on up-to-date bibliography.
Gerald Tenenbaum, Institut Elie Cartan, Vandoeuvre-les Nancy, France.
Elementary methods Some tools from real analysis Prime numbers Arithmetic functions Average orders Sieve methods Extremal orders The method of van der Corput Diophantine approximation Complex analysis methods The Euler gamma function Generating functions: Dirichlet series Summation formulae The Riemann zeta function The prime number theorem and the Riemann hypothesis The Selberg-Delange method Two arithmetic applications Tauberian theorems Primes in arithmetic progressions Probabilistic methods Densities Limiting distributions of arithmetic functions Normal order Distribution of additive functions and mean values of multiplicative functions Friable integers The saddle-point method Integers free of small factors Bibliography Index