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Analytic Number Theory: Exploring the Anatomy of Integers

Jean-Marie De Koninck Université Laval, Quebec, QC, Canada
Florian Luca Universidad Nacional Autonoma de México, Morelia, Michoacan, México
Available Formats:
Electronic ISBN: 978-0-8218-8541-3
Product Code: GSM/134.E
List Price: $75.00 MAA Member Price:$67.50
AMS Member Price: $60.00 Click above image for expanded view Analytic Number Theory: Exploring the Anatomy of Integers Jean-Marie De Koninck Université Laval, Quebec, QC, Canada Florian Luca Universidad Nacional Autonoma de México, Morelia, Michoacan, México Available Formats:  Electronic ISBN: 978-0-8218-8541-3 Product Code: GSM/134.E  List Price:$75.00 MAA Member Price: $67.50 AMS Member Price:$60.00
• Book Details

Volume: 1342012; 414 pp
MSC: Primary 11;

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.

Graduate students and research mathematicians interested in analytic number theory.

• Chapters
• 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

• Requests

Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 1342012; 414 pp
MSC: Primary 11;

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.

Graduate students and research mathematicians interested in analytic number theory.

• Chapters
• 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
Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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