A WebPage on The Erdos Distance Problem

by William Gasarch

(For now this is just papers that I want to gather in one place)

SURVEYS AND WRITEUPS

1. Julia Garibaldi and Alex Iosevich have a survey in progress: alexI.pdf It will one day be a book. See Alex Iosevich's website for updates.
2. Alex Iosevich has a nice exposition of the Szemeredi-Trotter theorem fouriergeom.ps
3. William Gasarch (oh, thats me!) has a writeup of the $n^{2/3}$ and $n^{4/5}$ results dist08.ps, dist08.pdf

POINTS IN THE PLANE:

1. Erdos. 1946. $n/\sqrt{\log n} \ge g_2(n) \ge \Omega(n^{0.5})$. erdos.pdf

2. Moser. 1952. $g_2(n) \ge \Omega(n^{0.66\ldots})$. moser.pdf (Actually $\Omega(n^{2/3})$)

3. Chung. 1984. $g_2(n) \ge \Omega(n^{0.7143\ldots})$. chung.pdf (Actually $\Omega(n^{5/7})$)

4. Chung, Szemeredi, Trotter. 1992. $g_2(n) \ge \Omega(n^{0.8}/\log n)$. CST.pdf

5. Szekely. 1993. $g_2(n) \ge \Omega(n^{0.8})$. szekely.pdf

6. Solymosi and Toth. 2001. $g_2(n) \ge \Omega(n^{0.8571})$. soly.ps Actaully $\Omega(n^{6/7})$.

7. Tardos, 2003. $g_2(n) \ge \Omega(n^{0.8634\ldots})$. tardos.pdf (Actually $\Omega(n^{(4e/(5e-1)) - \epsilon})$.)

8. Katz and Tardos. 2004. $g_2(n) \ge \Omega(n^{0.864\ldots})$. KT.ps Actually $\Omega(n^{((48-14e)/(55-16e)) - \epsilon})$

UPPER BOUNDS FOR POINTS IN THE PLANE.

1. Ford. One reference claimed this gave better upper bounds, but I don't see it. ford.pdf

LOWER BOUND FOR POINTS IN THREE-DIMENSIONAL SPACE

1. Aronov, Pach, Sharir, Tardos, 2002. $g_3(n) \ge \Omega(n^{0.546})$. APST.pdf Actually $n^{77/141 - \epsilon}$.