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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

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Table of Contents

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Front/Back Matter

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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