Arithmetic and polynomial progressions in the primes [after Gowers, Green, Tao and Ziegler]
Séminaire Bourbaki volume 2011/2012 exposés 1043-1058, Astérisque, no. 352 (2013), Exposé no. 1054, 39 p.
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Wolf, Julia. Arithmetic and polynomial progressions in the primes [after Gowers, Green, Tao and Ziegler], dans Séminaire Bourbaki volume 2011/2012 exposés 1043-1058, Astérisque, no. 352 (2013), Exposé no. 1054, 39 p. http://www.numdam.org/item/AST_2013__352__389_0/

[1] N. Alon - "Combinatorial Nullstellensatz", Combin. Probab. Comput. 8 (1999), nos. 1-2, p. 7-29. | DOI | Zbl

[2] P. T. Bateman & R. A. Horn - "A heuristic asymptotic formula concerning the distribution of prime numbers", Math. Comp. 16 (1962), p. 363-367. | DOI | Zbl

[3] F. A. Behrend - "On sets of integers which contain no three terms in arithmetical progression", Proc. Nat. Acad. Sci. U. S. A. 32 (1946), p. 331-332. | DOI | Zbl

[4] V. Bergelson - "Weakly mixing PET", Ergodic Theory Dynam. Systems 7 (1987), no. 3, p. 337-349. | DOI | Zbl

[5] V. Bergelson, B. Host & B. Kra - "Multiple recurrence and nilsequences", Invent. Math. 160 (2005), no. 2, p. 261-303. | DOI | Zbl

[6] V. Bergelson & A. Leibman - "Polynomial extensions of van der Waerden's and Szemerédi's theorems", J. Amer. Math. Soc. 9 (1996), no. 3, p. 725-753. | DOI | Zbl

[7] J. Bourgain - "On triples in arithmetic progression", Geom. Funct. Anal. 9 (1999), no. 5, p. 968-984. | DOI | Zbl

[8] D. Conlon & W. T. Gowers - "Combinatorial theorems in sparse random sets", preprint arXiv:1011.4310. | DOI | Zbl

[9] K. Conrad - "Irreducible values of polynomials: a non-analogy", in Number fields and function fields-two parallel worlds, Progr. Math., vol. 239, Birkhäuser, 2005, p. 71-85. | DOI | Zbl

[10] J.-P. Conze & E. Lesigne - "Sur un théorème ergodique pour des mesures diagonales", C. R. Acad. Sci. Paris Sér. I Math. 306 (1988), no. 12, p. 491-493. | Zbl

[11] J. G. Van Der Corput - "Über Summen von Primzahlen und Primzahlquadraten", Math. Ann. 116 (1939), p. 1-50. | DOI | EuDML | JFM | Zbl

[12] P. Erdös & P. Turán - "On Some Sequences of Integers", J. London Math. Soc. S1-11, no. 4, p. 261-264. | DOI | JFM

[13] G. A. Freĭman - Foundations of a structural theory of set addition, Translations of Mathematical Monographs, vol. 37, Amer. Math. Soc, 1973. | Zbl

[14] H. Furstenberg - "Ergodic behavior of diagonal measures and a theorem of Szemerédi on arithmetic progressions", J. Analyse Math. 31 (1977), p. 204-256. | DOI | Zbl

[15] H. Furstenberg & B. Weiss - "A mean ergodic theorem for (1/N) n=1 N f(T n x)g(T n 2 x)", in Convergence in ergodic theory and probability (Columbus, OH, 1993), Ohio State Univ. Math. Res. Inst. Publ., vol. 5, de Gruyter, 1996, p. 193-227. | Zbl

[16] D. A. Goldston & C. Y. Yildirim - "Higher correlations of divisor sums related to primes. III. Small gaps between primes", Proc. Lond. Math. Soc. 95 (2007), no. 3, p. 653-686. | DOI | Zbl

[17] W. T. Gowers - "A new proof of Szemerédi's theorem", Geom. Funct. Anal. 11 (2001), no. 3, p. 465-588. | DOI | Zbl

[18] W. T. Gowers, "Decompositions, approximate structure, transference, and the Hahn-Banach theorem", Bull. Lond. Math. Soc. 42 (2010), no. 4, p. 573-606. | DOI | Zbl

[19] W. T. Gowers & J. Wolf - "The true complexity of a system of linear equations", Proc. Lond. Math. Soc. 100 (2010), no. 1, p. 155-176. | DOI | Zbl

[20] W. T. Gowers & J. Wolf, "Linear forms and quadratic uniformity for functions on N ", J. Anal. Math. 115 (2011), p. 121-186. | DOI | Zbl

[21] B. Green - "On arithmetic structures in dense sets of integers", Duke Math. J. 114 (2002), no. 2, p. 215-238. | DOI | Zbl

[22] B. Green, "Roth's theorem in the primes", Ann. of Math. 161 (2005), no. 3, p. 1609-1636. | DOI | Zbl

[23] B. Green, "Long arithmetic progressions of primes", in Analytic number theory, Clay Math. Proc, vol. 7, Amer. Math. Soc., 2007, p. 149-167. | Zbl

[24] B. Green & T. Tao - "An inverse theorem for the Gowers U 3 (G) norm", Proc. Edinb. Math. Soc. 51 (2008), no. 1, p. 73-153. | DOI | Zbl

[25] B. Green & T. Tao, "The primes contain arbitrarily long arithmetic progressions", Ann. of Math. 167 (2008), no. 2, p. 481-547. | DOI | Zbl

[26] B. Green & T. Tao, "New bounds for Szemerédi's theorem. II. A new bound for r 4 (N)", in Analytic number theory, Cambridge Univ. Press, 2009, p. 180-204. | Zbl

[27] B. Green & T. Tao, "An arithmetic regularity lemma, an associated counting lemma, and applications", in An irregular mind, Bolyai Soc. Math. Stud., vol. 21, János Bolyai Math. Soc., 2010, p. 261-334. | DOI | Zbl

[28] B. Green & T. Tao, "The Möbius function is strongly orthogonal to nilsequences", Ann. of Math. 175 (2012), no. 2, p. 541-566. | DOI | Zbl

[29] B. Green, T. Tao & T. Ziegler - "An inverse theorem for the Gowers U s+1 [N]-norm", Electron. Res. Announc. Math. Sci. 18 (2011), p. 69-90. | Zbl

[30] B. Green, T. Tao & T. Ziegler, "An inverse theorem for the Gowers U s+1 [N]-norm", Ann. of Math. 176 (2012), no. 2, p. 1231-1372. | DOI | Zbl

[31] B. Green & T. Tao - "Linear equations in primes", Ann. of Math. 171 (2010), no. 3, p. 1753-1850. | DOI | Zbl

[32] M. Hamel & I. Łaba - "Arithmetic structures in random sets", Integers 8 (2008), p. A04, 21. | EuDML | Zbl

[33] B. Host - "Progressions arithmétiques dans les nombres premiers (d'après B. Green et T. Tao)", Séminaire Bourbaki, vol. 2004/2005, exposé n° 944, Astérisque 307 (2006), p. 229-246. | EuDML | Numdam | Zbl

[34] B. Host & B. Kra - "Nonconventional ergodic averages and nilmanifolds", Ann. of Math. 161 (2005), no. 1, p. 397-488. | DOI | Zbl

[35] Y. Kohayakawa, T. Łuczak & V. Rödl - "Arithmetic progressions of length three in subsets of a random set", Acta Arith. 75 (1996), no. 2, p. 133-163. | DOI | EuDML | Zbl

[36] B. Kra - "The Green-Tao theorem on arithmetic progressions in the primes: an ergodic point of view", Bull. Amer. Math. Soc. (N.S.) 43 (2006), no. 1, p. 3-23. | DOI | Zbl

[37] T. H. Lê - "Green-Tao theorem in function fields", Acta Arith. 147 (2011), no. 2, p. 129-152. | DOI | EuDML | Zbl

[38] J. Pintz, W. L. Steiger & E. Szemerédi - "On sets of natural numbers whose difference set contains no squares", J. London Math. Soc. 37 (1988), no. 2, p. 219-231. | DOI | Zbl

[39] O. Ramaré & I. Z. Ruzsa - "Additive properties of dense subsets of sifted sequences", J. Théor. Nombres Bordeaux 13 (2001), no. 2, p. 559-581. | DOI | EuDML | Numdam | Zbl

[40] O. Reingold, L. Trevisan, M. Tulsiani & S. Vadhan - "Dense subsets of pseudorandom sets", in 49th Annual IEEE Symposium on Foundations of Computer Science (FOCS), Philadephia, 2008, p. 76-85.

[41] K. F. Roth - "On certain sets of integers", J. London Math. Soc. 28 (1953), p. 104-109. | DOI | Zbl

[42] I. Z. Ruzsa - "Generalized arithmetical progressions and sumsets", Acta Math. Hungar. 65 (1994), no. 4, p. 379-388. | DOI | Zbl

[43] T. Sanders - "On Roth's theorem on progressions", Ann. of Math. 174 (2011), no. 1, p. 619-636. | DOI | Zbl

[44] T. Sanders, "On the Bogolyubov-Ruzsa lemma", Anal. PDE 5 (2012), no. 3, p. 627-655. | DOI | Zbl

[45] A. Sárkózy - "On difference sets of sequences of integers. I", Acta Math. Acad. Sci. Hungar. 31 (1978), nos. 1-2, p. 125-149. | DOI | Zbl

[46] T. Schoen & I. Shkredov - "Roth's theorem in many variables", preprint arXiv:1106.1601. | DOI | Zbl

[47] E. Szemerédi - "On sets of integers containing no k elements in arithmetic progression", Acta Arith. 27 (1975), p. 199-245. | DOI | EuDML | Zbl

[48] T. Tao - "The dichotomy between structure and randomness, arithmetic progressions, and the primes", in International Congress of Mathematicians. Vol. I, Eur. Math. Soc., Zürich, 2007, p. 581-608. | MR | Zbl

[49] T. Tao, "A remark on Goldston-Yildirim correlation estimates", http://www.math.ucla.edu/~tao/preprints/Expository/gy-corr.dvi.

[50] T. Tao & T. Ziegler - "The primes contain arbitrarily long polynomial progressions", Acta Math. 201 (2008), no. 2, p. 213-305. | DOI | MR | Zbl

[51] L. Trevisan, M. Tulsiani & S. Vadhan - "Regularity, boosting, and efficiently simulating every high-entropy distribution", in 24th Annual IEEE Conference on Computational Complexity, Paris, 2009, p. 126-136. | MR

[52] P. Varnavides - "On certain sets of positive density", J. London Math. Soc. 34 (1959), p. 358-360. | DOI | MR | Zbl

[53] I. M. Vinogradov - "Some theorems concerning the primes", Mat. Sbornik 2 (1937), p. 179-195. | EuDML | Zbl

[54] M. Walters - "Combinatorial proofs of the polynomial van der Waerden theorem and the polynomial Hales-Jewett theorem", J. London Math. Soc. 61 (2000), no. 1, p. 1-12. | DOI | MR | Zbl

[55] T. Ziegler - "Universal characteristic factors and Furstenberg averages", J. Amer. Math. Soc. 20 (2007), no. 1, p. 53-97. | DOI | MR | Zbl