Orient BlackSwan

About the BookAbout the AuthorTable of Contents

The authors assemble a fascinating collection of topics from analytic number theory that provides an introduction to the subject with a very clear and unique focus on the anatomy of integers, that is, on the study of the multiplicative structure of the integers. Some of the most important topics presented are the global and local behavior of arithmetic functions, an extensive study of smooth numbers, the Hardy–Ramanujan and Landau theorems, characters and the Dirichlet theorem, the abc conjecture along with some of its applications, and sieve methods. The book concludes with a whole chapter on the index of composition of an integer. One of this book’s best features is the collection of problems at the end of each chapter that have been chosen carefully to reinforce the material. The authors include solutions to the even-numbered problems, making this volume very appropriate for readers who want to test their understanding of the theory presented in the book

Jean-Marie De Koninck is Professor of Mathematics at Université Laval, Quebec City, Canada.

Florian Luca is Doctor en Matemáticas at the Centro de Ciencias Matemáticas, Universidad Nacional Autonoma de México, Morelia, México.

Preface

Chapter 1. Preliminary Notions

Chapter 2. Prime Numbers and Their Properties

Chapter 3. The Riemann Zeta Function

Chapter 4. Setting the Stage for the Proof of the Prime Number

Chapter 5. The Proof of the Prime Number Theorem

Chapter 6. The Global Behavior of Arithmetic Functions

Chapter 7. The Local Behavior of Arithmetic Functions

Chapter 8. The Fascinating Euler Function

Chapter 9. Smooth Numbers

Chapter 10. The Hardy–Ramanujan and Landau Theorems

Chapter 11. The abc Conjecture and Some of Its Applications

Chapter 12. Sieve Methods

Chapter 13. Prime Numbers in Arithmetic Progression

Chapter 14. Characters and the Dirichlet Theorem

Chapter 15. Selected Applications of Primes in Arithmetic Progression

Chapter 16. The Index of Composition of an Integer

Appendix: Basic Complex Analysis Theory

Bibliography

Index