Sum-product phenomena in F_p: a brief introduction

Details Sum-product phenomena in F_p: a brief introduction Sum-product phenomena in F_p: a brief introduction

2009-04-14

arxiv.org/abs/0904.2075v1

Mathematics

Number Theory

10 pages, not for publication

Scientific paper

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 The arguments are essentially extracted from a paper of Bourgain, and I benefitted very much from being in receipt of unpublished course notes of Elon Lindenstrauss.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.

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