Arithmetic progressions in sumsets

Geometric and Functional Analysis

Volumn 12, Issue 3, 2002, Pages 584-597

  Green, B ^a  

^a TRINITY COLLEGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035995720     PISSN: 1016443X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00039-002-8258-4     Document Type: Article

References (12)

1. [B] S. Bernstein, Sur une modification de l'inéqualité de Tchebichef, Annal. Sci. Inst. Sav. Ukr. Sect. Math. I (1924).
2. [Bo] N.N. Bogolubov, Some algebraic properties of almost periods, Zap. Kafedry Mat. Fiz. Kiev 4 (1939), 185-194 (in Russian).
3. [Bou1] J. Bourgain, On arithmetic progressions in sums of sets of integers, in "A Tribute to Paul Erdos", CUP (1990), 105-109.
4. [Bou2] J. Bourgain, On triples in arithmetic progression, GAFA, Geom. funct. anal. 9:5 (1999), 968-984.
5. [C] M.C. Chang, Polynomial bounds for Freimans's theorem, Duke Math. Jour., to appear.
6. [FHR] G.A. Freiman, H. Halberstam, I.Z. Ruzsa, Integer sum sets containing long arithmetic progressions, J. London Math. Soc. (2) 46 (1992), 193-201.
7. [G] W.T. Gowers, A new proof of Szemerédi's theorem, GAFA, Geom. funct. anal. 11:3 (2001), 465-588.
8. [Gr1] B.J. Green, Bernstein's inequality and Hoeffding's inequality, available at http://www.dpmms.cam.ac.uk/~bjg23/expos.html.
9. [Gr2] B.J. Green, Edinburgh lecture notes on Freiman's theorem, available at http://www.dpmms.cam.ac.uk/~bjg23/preprints.html.
10. [Gr3] B.J. Green, Some constructions in the inverse spectral theory of cyclic groups, Combinatorics, Probability and Computing, to appear; available at http://www.dpmms.cam.ac.uk/~bjg23/preprints.html.
11. [R] W. Rudin, Fourier Analysis on Groups, Wiley 1990 (reprint of the 1962 original).
12. [Ru] I.Z. Ruzsa, Arithmetic progressions in sumsets, Acta Arith. 60:2 (1991), 191-202.