New results on the Erdös–Szemerédi sum-product problems

Mei-Chu Chang

doi:10.1016/S1631-073X(03)00018-9

Combinatorics

New results on the Erdös–Szemerédi sum-product problems
[Nouveaux résultats sur les problèmes sommes-produits d'Erdös et Szemerédi]

Présenté par : Jean Bourgain

Mei-Chu Chang ¹

¹ University of California at Riverside, Department of Mathematics, Riverside, CA 92521, USA

Comptes Rendus. Mathématique, Volume 336 (2003) no. 3, pp. 201-205.

Résumé
Abstract

Dans cette Note, nous présentons diverses contributions (ou solutions) à des questions concernant la taille d'ensembles somme et produit d'ensembles finis d'entiers (ou de nombres complexes), posées dans [8]. Nous introduisons également quelques méthodes nouvelles dans ce domaine de recherche.

In this Note, we present several contributions (or solutions) to problems related to the sizes of sum sets and product sets of integers (or complex numbers), considered in [8]. We also introduce some new methods in this area of research.

Reçu le : 2002-07-12
Accepté le : 2002-07-17
Publié le : 2003-02-01

DOI : 10.1016/S1631-073X(03)00018-9

Affiliations des auteurs :

Mei-Chu Chang ¹

¹ University of California at Riverside, Department of Mathematics, Riverside, CA 92521, USA

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     title = {New results on the {Erd\"os{\textendash}Szemer\'edi} sum-product problems},
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Mei-Chu Chang. New results on the Erdös–Szemerédi sum-product problems. Comptes Rendus. Mathématique, Volume 336 (2003) no. 3, pp. 201-205. doi : 10.1016/S1631-073X(03)00018-9. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00018-9/

Bibliographie
Cité par

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[8] P. Erdös, E. Szemerédi, On sums and products of integers, in: P. Erdös, L. Alpàr, G. Haláz (Eds.), Stud. Pure Math., pp. 215–218

[9] Laczkovich, I. Ruzsa, Preprint

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[12] E. Szemerédi; W. Trotter Extremal problems in discrete geometry, Combinatorics, Volume 3 (1983) no. 3–4, pp. 387-392

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