V. Bergelson, Weakly mixing PET. Ergodic Theory Dynam, Systems, vol.7, issue.3, pp.337-349, 1987.

N. Frantzikinakis, M. Johnson, E. Lesigne, A. M. Wierdl-[-be2, and ]. V. Bergelson, Combinatorial and Diophantine applications of ergodic theory. Appendix A by A. Leibman and Appendix B by A. Quas and M. Wierdl. Handbook of dynamical systems, pp.745-869, 2006.

M. Boshernitzan, G. Kolesnik, A. Quas, and M. , Ergodic averaging sequences, Journal d'Analyse Math??matique, vol.29, issue.no. 16, pp.63-103, 2005.
DOI : 10.1007/BF02791497

]. J. Bou and . Bourgain, On the maximal ergodic theorem for certain subsets of the integers, Israel J. Math, pp.61-100, 1988.

J. Deshouillers, P. Erdös, and A. Sárközy, On additive bases, Acta Arith, vol.30, issue.2, pp.121-132, 1976.

J. Deshouillers and E. Fouvry, On Additive Bases (II), Journal of the London Mathematical Society, vol.2, issue.3, pp.14-413, 1976.
DOI : 10.1112/jlms/s2-14.3.413

N. Frantzikinakis, E. Lesigne, and M. , Ensembles de k-r??currence mais pas de k+1-r??currence, Annales de l???institut Fourier, vol.56, issue.4
DOI : 10.5802/aif.2202

N. Frantzikinakis, E. Lesigne, and M. , Powers of sequences and recurrence, Proc. Lond, pp.504-530, 2009.
DOI : 10.1112/plms/pdn040

URL : https://hal.archives-ouvertes.fr/hal-00276737

B. Host and B. Kra, Nonconventional ergodic averages and nilmanifolds, Annals of Mathematics, vol.161, issue.1, pp.397-488, 2005.
DOI : 10.4007/annals.2005.161.397

URL : https://hal.archives-ouvertes.fr/hal-01267075

B. Host and B. Kra, Convergence of polynomial ergodic averages, Israel Journal of Mathematics, vol.2, issue.1, pp.1-19, 2005.
DOI : 10.1007/BF02772534

B. Host and B. Kra, Uniformity seminorms on l ? and spplications, To appear J. Anal. Math. Available at

. L. Kn, H. Kuipers, and . Niederreiter, Uniform distribution of sequences. Pure and Applied Mathematics, 1974.

]. A. Lei and . Leibman, Convergence of multiple ergodic averages along polynomials of several variables, Isr. J. Math, vol.146, pp.303-316, 2005.

M. [. Rosenblatt, . Wierdlv-]-r, and . Vaughan, Pointwise theorems via harmonic analysis Ergodic theory and its connections with harmonic analysis (Alexandria, 1993) London Math. Soc. Lecture Note Ser The Hardy-Littlewood method Universal characteristic factors and Furstenberg averages, Cambridge Tracts in Mathematics J. Amer. Math. Soc, vol.205, issue.20, pp.3-151, 1997.