Introduction to Analytic and Probabilistic Number Theory

Includes index

Includes bibliographical references

Part I. Elementary Methods: Some tools from real analysis 1. Prime numbers 2. Arithmetic functions 3. Average orders 4. Sieve methods 5. Extremal orders 6. The method of van der Corput Part II. Methods of Complex Analysis: 1. Generating functions: Dirichlet series 2. Summation formulae 3. The Riemann zeta function 4. The Prime Number Theorem and the Riemann Hypothesis 5. The Selberg-Delange method 6. Two arithmetic applications 7. Tauberian theorems 8. Prime numbers in arithmetic progressions Part III. Probabilistic Methods: 1. Densities 2. Limiting distribution of arithmetic functions 3. Normal order 4. Distribution of additive functions and mean values of multiplicative functions 5. Integers free of large prime factors. The saddle-point method 6. Integers free of small prime factors

This is a self-contained introduction to analytic methods in number theory. It offers to students and those beginning research a systematic and consistent account of the subject but will also be a convenient resource and reference for more experienced mathematicians.