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.
Preface
Notation
Frequently used functions
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 theorem
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
Solutions to even-numbered problems
Bibliography
Index
Jean-Marie De Koninck, Université Laval, Quebec, QC, Canada
Florian Luca Universidad Nacional Autonoma de México, Morelia, Michoacan, México
