**Graduate Studies in Mathematics**

Volume: 134;
2012;
414 pp;
Hardcover

MSC: Primary 11;

Print ISBN: 978-0-8218-7577-3

Product Code: GSM/134

List Price: $75.00

Individual Member Price: $60.00

**Electronic ISBN: 978-0-8218-8541-3
Product Code: GSM/134.E**

List Price: $75.00

Individual Member Price: $60.00

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#### Supplemental Materials

# Analytic Number Theory: Exploring the Anatomy of Integers

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*Jean-Marie De Koninck; Florian Luca*

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.

#### Table of Contents

# Table of Contents

## Analytic Number Theory: Exploring the Anatomy of Integers

- Cover Cover11 free
- Title page i2 free
- Contents iii4 free
- Preface ix10 free
- Notation xiii14 free
- Frequently used functions xvii18 free
- Chapter 1. Preliminary notions 120 free
- Chapter 2. Prime numbers and their properties 1938
- Chapter 3. The Riemann zeta function 3958
- Chapter 4. Setting the stage for the proof of the prime number theorem 5170
- Chapter 5. The proof of the prime number theorem 6382
- Chapter 6. The global behavior of arithmetic functions 7594
- Chapter 7. The local behavior of arithmetic functions 93112
- Chapter 8. The fascinating Euler function 115134
- Chapter 9. Smooth numbers 127146
- Chapter 10. The Hardy-Ramanujan and Landau theorems 157176
- Chapter 11. The 𝑎𝑏𝑐 conjecture and some of its applications 167186
- Chapter 12. Sieve methods 179198
- Chapter 13. Prime numbers in arithmetic progression 217236
- Chapter 14. Characters and the Dirichlet theorem 233252
- Chapter 15. Selected applications of primes in arithmetic progression 251270
- Chapter 16. The index of composition of an integer 267286
- Appendix. Basic complex analysis theory 281300
- Solutions to even-numbered problems 291310
- Bibliography 405424
- Index 413432 free
- Back Cover Back Cover1434

#### Readership

Graduate students and research mathematicians interested in analytic number theory.