Comptes Rendus
no. 11-12
Combinatorics/Number Theory
Some consequences of the Polynomial Freiman–Ruzsa Conjecture
Presented by: Jean Bourgain
Mei-Chu Chang1
1Department of Mathematics, University of California, Riverside, CA 92521, USA
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).

Received:
Accepted:
Published online:
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

[1] J. Bourgain Estimates on exponential sums related to Diffie–Hellman distributions, GAFA, Volume 15 (2005) no. 1, pp. 1-34

[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

[4] M.-C. Chang A polynomial bound in Freiman's Theorem, Duke Math. J., Volume 113 (2002) no. 3, pp. 399-419

[5] M.-C. Chang Product theorems in SL2 and SL3, J. Math. Jussieu, Volume 7 (2008) no. 1, pp. 1-25

[6] M.-C. Chang, On product sets in SL2 and SL3, preprint

[7] J.-H. Evertse; H. Schlickewei; W. Schmidt Linear equations in variables which lie in a multiplicative group, Ann. Math., Volume 155 (2002), pp. 807-836

[8] H. Helfgott, Growth and generation in SL3(Z/Zp), preprint, 2008

[9] T. Tao; V. Vu Additive Combinatorics, Cambridge University Press, 2006

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