Sum-product phenomena in F_p: a brief introduction

Ben Green

Sum-product phenomena in F_p: a brief introduction

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arxiv 0904.2075 v1 pith:STQUOIRN submitted 2009-04-14 math.NT math.CO

Ben Green This is my paper · ORCID

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 The arguments are essentially extracted from a paper of Bourgain, and I benefitted very much from being in receipt of unpublished course notes of Elon Lindenstrauss.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