In this short note we establish new refinements of multidimensional Szemerédi and polynomial Van der Waerden theorems along the shifted primes.
Nous présentons de nouveaux résultats du type Szemerédi multidimensionnel et Van der Waerden polynomial multidimensionnel le long des ensembles et .
Accepted:
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Vitaly Bergelson 1; Alexander Leibman 1; Tamar Ziegler 2
@article{CRMATH_2011__349_3-4_123_0,
author = {Vitaly Bergelson and Alexander Leibman and Tamar Ziegler},
title = {The shifted primes and the multidimensional {Szemer\'edi} and polynomial {Van} der {Waerden} theorems},
journal = {Comptes Rendus. Math\'ematique},
pages = {123--125},
publisher = {Elsevier},
volume = {349},
number = {3-4},
year = {2011},
doi = {10.1016/j.crma.2010.11.028},
language = {en},
}
TY - JOUR AU - Vitaly Bergelson AU - Alexander Leibman AU - Tamar Ziegler TI - The shifted primes and the multidimensional Szemerédi and polynomial Van der Waerden theorems JO - Comptes Rendus. Mathématique PY - 2011 SP - 123 EP - 125 VL - 349 IS - 3-4 PB - Elsevier DO - 10.1016/j.crma.2010.11.028 LA - en ID - CRMATH_2011__349_3-4_123_0 ER -
%0 Journal Article %A Vitaly Bergelson %A Alexander Leibman %A Tamar Ziegler %T The shifted primes and the multidimensional Szemerédi and polynomial Van der Waerden theorems %J Comptes Rendus. Mathématique %D 2011 %P 123-125 %V 349 %N 3-4 %I Elsevier %R 10.1016/j.crma.2010.11.028 %G en %F CRMATH_2011__349_3-4_123_0
Vitaly Bergelson; Alexander Leibman; Tamar Ziegler. The shifted primes and the multidimensional Szemerédi and polynomial Van der Waerden theorems. Comptes Rendus. Mathématique, Volume 349 (2011) no. 3-4, pp. 123-125. doi : 10.1016/j.crma.2010.11.028. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.11.028/
[1] Ergodic theory and Diophantine problems, Temuco, 1997 (London Math. Soc. Lecture Note Ser.), Volume vol. 279, Cambridge Univ. Press, Cambridge (2000), pp. 167-205
[2] Polynomial Van der Waerden and Szemerédi theorems, J. Amer. Math. Soc., Volume 9 (1996), pp. 725-753
[3] Set-polynomials and polynomial extension of the Hales–Jewett theorem, Ann. of Math. (2), Volume 150 (1999) no. 1, pp. 33-75
[4] Recurrence for semigroup actions and a non-commutative Schur theorem, Minneapolis, MN, 1995 (Contemp. Math.), Volume vol. 215, Amer. Math. Soc., Providence, RI (1998), pp. 205-222
[5] Multiple recurrence and convergence for sequences related to the prime numbers, J. Reine Angew. Math., Volume 611 (2007), pp. 131-144
[6] An ergodic Szemerédi theorem for IP-systems and combinatorial theory, J. Anal. Math., Volume 45 (1985), pp. 117-168
[7] Topological dynamics and combinatorial number theory, J. Anal. Math., Volume 34 (1978), pp. 61-85
[8] Linear equations in primes, Ann. of Math. (2), Volume 171 (2010) no. 3, pp. 1753-1850
[9] B. Green, T. Tao, The Möbius function is strongly orthogonal to nilsequences, Ann. of Math., in press.
[10] B. Green, T. Tao, T. Ziegler, An inverse theorem for the Gowers norm, preprint.
[11] Elemental Methods in Ergodic Ramsey Theory, Lecture Notes in Math., vol. 1722, Springer-Verlag, Berlin, 1999
[12] T. Wooley, T. Ziegler, Multiple recurrence and convergence along the primes, Amer. J. Math., in press.
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☆ The first and the third authors are supported by BSF grant No. 2006094. The first and the second authors are supported by NSF grant DMS-0901106.
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