Comptes Rendus
Combinatorics/Number Theory
Some consequences of the Polynomial Freiman–Ruzsa Conjecture
[Quelques conséquences de la conjecture polynomiale de Freiman–Ruzsa]
Comptes Rendus. Mathématique, Volume 347 (2009) no. 11-12, pp. 583-588.

Assuming the Weak Polynomial Freiman–Ruzsa Conjecture, we derive some consequences on sum-products and the growth of subsets of SL3(C).

En supposant la conjecture polynomiale faible de Freiman–Ruzsa, on en déduit certaines conséquences sur les ensembles sommes-produits ainsi que sur la croissance de sous-ensembles de SL3(C).

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.04.006

Mei-Chu Chang 1

1 Department of Mathematics, University of California, Riverside, CA 92521, USA
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Mei-Chu Chang. Some consequences of the Polynomial Freiman–Ruzsa Conjecture. Comptes Rendus. Mathématique, Volume 347 (2009) no. 11-12, pp. 583-588. doi : 10.1016/j.crma.2009.04.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.04.006/

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[2] J. Bourgain; M.-C. Chang On the size of k-fold sum and product sets of integers, JAMS, Volume 17 (2004) no. 2, pp. 473-497

[3] J. Bourgain, M.-C. Chang, Sum-product theorems in algebraic number fields, Journal d'Analyse Mathematique, in press

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