Sum-product theorems and incidence geometry
Mei-Chu Chang, József Solymosi · Journal of the European Mathematical Society · 2007
In this paper we prove the following theorems in incidence geometry. The main ingredients used are the subspace theorem, Balog–Szemerédi–Gowers Theorem, and Szemerédi–Trotter Theorem. We also generalize the theorems to high dimensions, extend Theorem 1 to \Bbb F_p^2 , and give the version of Theorem 2 over \Bbb Q .