Polynomial szemerédi theorems for countable modules over integral domains and finite fields

Journal d'Analyse Mathematique

Volumn 95, Issue , 2005, Pages 243-296

  Bergelson, V ^a   Leibman, A ^a   Mccutcheon, R ^b  

^a OHIO STATE UNIVERSITY   (United States)

^b University of Memphis   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 22144449233     PISSN: 00217670     EISSN: 15658538     Source Type: Journal    
DOI: 10.1007/BF02791504     Document Type: Article

References (18)

1. [B1] V. Bergelson, Weakly mixing PET, Ergodic Theory Dynam. Systems 7 (1987), 337-349.
2. [B2] V. Bergelson, Ergodic theory and Diophantine problems, in Topics in Symbolic Dynamics and Applications, London Math. Soc. Lecture Note Ser. 279 (2000), 167-205.
3. [BFM] V. Bergelson, H. Furstenberg and R. McCutcheon, IP sets and polynomial recurrence, Ergodic Theory Dynam. Systems 16 (1996), 963-974.
4. [BL1] V. Bergelson and A. Leibman, Polynomial extensions of van der Waerden's and Szemerédi's theorems, J. Amer. Math. Soc. 9 (1996), 725-753.
5. [BL2] V. Bergelson and A. Leibman, Set-polynomials and polynomial extension of the Hales-Jewett theorem, Ann. of Math. (2) 150 (1999), 33-75.
6. d-actions, London Math. Soc. Lecture Note Ser. 228 (1996), 273-296.
7. [BMZ] V. Bergelson, R. McCutcheon and Q. Zhang, A Roth theorem for amenable groups, Amer. J. Math. 119 (1997), 1173-1211.
8. [F1] H. Furstenberg, Ergodic behavior of diagonal measures and a theorem of Szemerédi on arithmetic progressions, J. Analyse Math. 31 (1977), 204-256.
9. [F2] H. Furstenberg, Recurrence in Ergodic Theory and Combinatorial Number Theory, Princeton University Press, 1981.
10. [FK1] H. Furstenberg and Y. Katznelson, An ergodic Szemerédi theorem for commuting transformations, J. Analyse Math. 34 (1978), 275-291.
11. [FK2] H. Furstenberg and Y. Katznelson, An ergodic Szemerédi theorem for IP-systems and combinatorial theory, J. Analyse Math. 45 (1985), 117-168.
12. [FK3] H. Furstenberg and Y. Katznelson, A density version of the Hales-Jewett theorem, J. Analyse Math. 57 (1991), 64-119.
13. [G] W. T. Gowers, A new proof of Szemerédi's theorem, Geom. Funct. Anal. 11 (2001), 465-588.
14. [La] P. Larick, Ph.D. Thesis, The Ohio State University, 1998.
15. [Le] A. Leibman, Multiple recurrence theorem for measure preserving actions of a nilpotent group, Geom. Funct. Anal. 8 (1998), 853-931.
16. [Sz] E. Szemerédi, On sets of integers containing no k elements in arithmetic progression, Acta Arith. 27 (1975), 199-245.
17. [Z1] R. Zimmer, Extensions of ergodic group actions, Illinois J. Math. 20 (1976), 373-409.
18. [Z2] R. Zimmer, Ergodic actions with generalized discrete spectrum, Illinois J. Math. 20 (1976), 555-588.