AMS eBook CollectionsOne of the world's most respected mathematical collections, available in digital format for your library or institution

Beurling Generalized Numbers

About this Title

Harold G. Diamond, University of Illinois, Urbana, IL and Wen-Bin Zhang (Cheung Man Ping), University of the West Indies, Kingston, Jamaica

Publication: Mathematical Surveys and Monographs
Publication Year: 2016; Volume 213
ISBNs: 978-1-4704-3045-0 (print); 978-1-4704-3538-7 (online)
DOI: https://doi.org/10.1090/surv/213
MathSciNet review: MR3559358
MSC: Primary 11N80

View full volume as PDF

Read more about this volume

Table of Contents

Download chapters as PDF

Front/Back Matter

• View this volume's front and back matter

Chapters

• Chapter 1. Overview
• Chapter 2. Analytic machinery
• Chapter 3. $\mathbf {dN}$ as an exponential and Chebyshev’s identity
• Chapter 4. Upper and lower estimates of $\mathbf {N(x)}$
• Chapter 5. Mertens’ formulas and logarithmic density
• Chapter 6. O-density of g-integers
• Chapter 7. Density of g-integers
• Chapter 8. Simple estimates of $\mathbf {\pi (x)}$
• Chapter 9. Chebyshev bounds—Elementary theory
• Chapter 10. Wiener-Ikehara Tauberian theorems
• Chapter 11. Chebyshev bounds—Analytic methods
• Chapter 12. Optimality of a Chebyshev bound
• Chapter 13. Beurling’s PNT
• Chapter 14. Equivalences to the PNT
• Chapter 15. Kahane’s PNT
• Chapter 16. PNT with remainder
• Chapter 17. Optimality of the dlVP remainder term
• Chapter 18. The Dickman and Buchstab functions