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

# The Erdős Distance Problem

### About this Title

**Julia Garibaldi**, **Alex Iosevich**, *University of Rochester, Rochester, NY* and **Steven Senger**

Publication: The Student Mathematical Library

Publication Year
2011: Volume 56

ISBNs: 978-0-8218-5281-1 (print); 978-1-4704-1639-3 (online)

DOI: http://dx.doi.org/10.1090/stml/056

MathSciNet review: MR2721878

MSC: Primary 52-01; Secondary 05-01, 11-01, 42-01, 51-01

### Table of Contents

**Front/Back Matter**

**Chapters**

- Introduction
- Chapter 1. The $\sqrt {n}$ theory
- Chapter 2. The $n^{2/3}$ theory
- Chapter 3. The Cauchy-Schwarz inequality
- Chapter 4. Graph theory and incidences
- Chapter 5. The $n^{4/5}$ theory
- Chapter 6. The $n^{6/7}$ theory
- Chapter 7. Beyond $n^{6/7}$
- Chapter 8. Information theory
- Chapter 9. Dot products
- Chapter 10. Vector spaces over finite fields
- Chapter 11. Distances in vector spaces over finite fields
- Chapter 12. Applications of the Erdős distance problem
- Appendix A. Hyperbolas in the plane
- Appendix B. Basic probability theory
- Appendix C. Jensen’s inequality