AMS eBook CollectionsOne of the world's most respected mathematical collections, available in digital format for your library or institution
Analytic Number Theory: Exploring the Anatomy of Integers
About this Title
Jean-Marie De Koninck, Université Laval, Quebec, QC, Canada and Florian Luca, Universidad Nacional Autonoma de México, Morelia, Michoacan, México
Publication: Graduate Studies in Mathematics
Publication Year:
2012; Volume 134
ISBNs: 978-0-8218-7577-3 (print); 978-0-8218-8541-3 (online)
DOI: https://doi.org/10.1090/gsm/134
MathSciNet review: MR2919246
MSC: Primary 11Nxx; Secondary 11A05, 11A41, 11B05, 11K65
Table of Contents
Download chapters as PDF
Front/Back Matter
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