Sum-product phenomena in F_p: a brief introduction
Number Theory
2009-04-15 v1 Combinatorics
Abstract
These notes arose from my Cambridge Part III course on Additive Combinatorics, given in Lent Term 2009. The aim was to understand the simplest proof of the Bourgain-Glibichuk-Konyagin bounds for exponential sums over subgroups. As a byproduct one obtains a clean proof of the Bourgain-Katz-Tao theorem on the sum-product phenomenon in F_p. The arguments are essentially extracted from a paper of Bourgain, and I benefitted very much from being in receipt of unpublished course notes of Elon Lindenstrauss. No originality is claimed.
Keywords
Cite
@article{arxiv.0904.2075,
title = {Sum-product phenomena in F_p: a brief introduction},
author = {Ben Green},
journal= {arXiv preprint arXiv:0904.2075},
year = {2009}
}
Comments
10 pages, not for publication