Analytic Number Theory

Exploring the Anatomy of Integers

Jean-Marie De Koninck, Florian Luca (Autoren)

Buch | Hardcover

414 Seiten

2012
American Mathematical Society (Verlag)
978-0-8218-7577-3 (ISBN)

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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, Université Laval, Quebec, QC, Canada Florian Luca Universidad Nacional Autonoma de México, Morelia, Michoacan, México

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

Erscheint lt. Verlag	13.9.2012
Reihe/Serie	Graduate Studies in Mathematics
Verlagsort	Providence
Sprache	englisch
Gewicht	906 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
ISBN-10	0-8218-7577-9 / 0821875779
ISBN-13	978-0-8218-7577-3 / 9780821875773
Zustand	Neuware