A quantified version of Bourgain's sum-product estimate in \(\mathbb F_{p}\) for subsets of incomparable sizes
type: Item
instance of: scholarly article
title: A quantified version of Bourgain's sum-product estimate in \(\mathbb F_{p}\) for subsets of incomparable sizes
zbMATH Open document ID: 1206.11031
author: Moubariz Z. Garaev
published in: The Electronic Journal of Combinatorics
publication date: 2009-04-07T00:00:00Z
full work available at URL: https://eudml.org/doc/117242
full work available at URL: v15i1r58.html
review text: Summary: Let \({\mathbb F}_p\) be the field of residue classes modulo a prime number \(p\). In this paper we prove that if \(A,B\subset {\mathbb F}_p^*,\) then for any fixed \(\varepsilon>0,\) \[ |A+A|+|AB|\gg \left(\min \left\{|B|, \frac{p}{|A|}\right\}\right)^{1/25-\varepsilon}|A|. \] This quantifies \textit{J. Bourgain}'s recent sum-product estimate [Int. J. Number Theory 1, No. 1, 1--32 (2005; Zbl 1173.11310)].
Mathematics Subject Classification ID: 11B75
Mathematics Subject Classification ID: 11T23
zbMATH DE Number: 5540963
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5540963