@incollection{AST_2013__352__389_0,
author = {Wolf, Julia},
title = {Arithmetic and polynomial progressions in the primes [after {Gowers,} {Green,} {Tao} and {Ziegler]}},
booktitle = {S\'eminaire Bourbaki volume 2011/2012 expos\'es 1043-1058},
series = {Ast\'erisque},
note = {talk:1054},
pages = {389--427},
year = {2013},
publisher = {Soci\'et\'e math\'ematique de France},
number = {352},
zbl = {1295.11099},
language = {en},
url = {https://www.numdam.org/item/AST_2013__352__389_0/}
}
TY - CHAP AU - Wolf, Julia TI - Arithmetic and polynomial progressions in the primes [after Gowers, Green, Tao and Ziegler] BT - Séminaire Bourbaki volume 2011/2012 exposés 1043-1058 AU - Collectif T3 - Astérisque N1 - talk:1054 PY - 2013 SP - 389 EP - 427 IS - 352 PB - Société mathématique de France UR - https://www.numdam.org/item/AST_2013__352__389_0/ LA - en ID - AST_2013__352__389_0 ER -
%0 Book Section %A Wolf, Julia %T Arithmetic and polynomial progressions in the primes [after Gowers, Green, Tao and Ziegler] %B Séminaire Bourbaki volume 2011/2012 exposés 1043-1058 %A Collectif %S Astérisque %Z talk:1054 %D 2013 %P 389-427 %N 352 %I Société mathématique de France %U https://www.numdam.org/item/AST_2013__352__389_0/ %G en %F AST_2013__352__389_0
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.. https://www.numdam.org/item/AST_2013__352__389_0/
[1] - "Combinatorial Nullstellensatz", Combin. Probab. Comput. 8 (1999), nos. 1-2, p. 7-29. | Zbl | DOI
[2] & - "A heuristic asymptotic formula concerning the distribution of prime numbers", Math. Comp. 16 (1962), p. 363-367. | Zbl | DOI
[3] - "On sets of integers which contain no three terms in arithmetical progression", Proc. Nat. Acad. Sci. U. S. A. 32 (1946), p. 331-332. | Zbl | DOI
[4] - "Weakly mixing PET", Ergodic Theory Dynam. Systems 7 (1987), no. 3, p. 337-349. | Zbl | DOI
[5] , & - "Multiple recurrence and nilsequences", Invent. Math. 160 (2005), no. 2, p. 261-303. | Zbl | DOI
[6] & - "Polynomial extensions of van der Waerden's and Szemerédi's theorems", J. Amer. Math. Soc. 9 (1996), no. 3, p. 725-753. | Zbl | DOI
[7] - "On triples in arithmetic progression", Geom. Funct. Anal. 9 (1999), no. 5, p. 968-984. | Zbl | DOI
[8] & - "Combinatorial theorems in sparse random sets", preprint arXiv:1011.4310. | Zbl | DOI
[9] - "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. | Zbl | DOI
[10] & - "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] - "Über Summen von Primzahlen und Primzahlquadraten", Math. Ann. 116 (1939), p. 1-50. | Zbl | EuDML | JFM | DOI
[12] & - "On Some Sequences of Integers", J. London Math. Soc. S1-11, no. 4, p. 261-264. | JFM | DOI
[13] - Foundations of a structural theory of set addition, Translations of Mathematical Monographs, vol. 37, Amer. Math. Soc, 1973. | Zbl
[14] - "Ergodic behavior of diagonal measures and a theorem of Szemerédi on arithmetic progressions", J. Analyse Math. 31 (1977), p. 204-256. | Zbl | DOI
[15] & - "A mean ergodic theorem for ", 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] & - "Higher correlations of divisor sums related to primes. III. Small gaps between primes", Proc. Lond. Math. Soc. 95 (2007), no. 3, p. 653-686. | Zbl | DOI
[17] - "A new proof of Szemerédi's theorem", Geom. Funct. Anal. 11 (2001), no. 3, p. 465-588. | Zbl | DOI
[18] , "Decompositions, approximate structure, transference, and the Hahn-Banach theorem", Bull. Lond. Math. Soc. 42 (2010), no. 4, p. 573-606. | Zbl | DOI
[19] & - "The true complexity of a system of linear equations", Proc. Lond. Math. Soc. 100 (2010), no. 1, p. 155-176. | Zbl | DOI
[20] & , "Linear forms and quadratic uniformity for functions on ", J. Anal. Math. 115 (2011), p. 121-186. | Zbl | DOI
[21] - "On arithmetic structures in dense sets of integers", Duke Math. J. 114 (2002), no. 2, p. 215-238. | Zbl | DOI
[22] , "Roth's theorem in the primes", Ann. of Math. 161 (2005), no. 3, p. 1609-1636. | Zbl | DOI
[23] , "Long arithmetic progressions of primes", in Analytic number theory, Clay Math. Proc, vol. 7, Amer. Math. Soc., 2007, p. 149-167. | Zbl
[24] & - "An inverse theorem for the Gowers norm", Proc. Edinb. Math. Soc. 51 (2008), no. 1, p. 73-153. | Zbl | DOI
[25] & , "The primes contain arbitrarily long arithmetic progressions", Ann. of Math. 167 (2008), no. 2, p. 481-547. | Zbl | DOI
[26] & , "New bounds for Szemerédi's theorem. II. A new bound for ", in Analytic number theory, Cambridge Univ. Press, 2009, p. 180-204. | Zbl
[27] & , "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. | Zbl | DOI
[28] & , "The Möbius function is strongly orthogonal to nilsequences", Ann. of Math. 175 (2012), no. 2, p. 541-566. | Zbl | DOI
[29] , & - "An inverse theorem for the Gowers -norm", Electron. Res. Announc. Math. Sci. 18 (2011), p. 69-90. | Zbl
[30] , & , "An inverse theorem for the Gowers -norm", Ann. of Math. 176 (2012), no. 2, p. 1231-1372. | Zbl | DOI
[31] & - "Linear equations in primes", Ann. of Math. 171 (2010), no. 3, p. 1753-1850. | Zbl | DOI
[32] & - "Arithmetic structures in random sets", Integers 8 (2008), p. A04, 21. | Zbl | EuDML
[33] - "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. | Zbl | EuDML | Numdam
[34] & - "Nonconventional ergodic averages and nilmanifolds", Ann. of Math. 161 (2005), no. 1, p. 397-488. | Zbl | DOI
[35] , & - "Arithmetic progressions of length three in subsets of a random set", Acta Arith. 75 (1996), no. 2, p. 133-163. | Zbl | EuDML | DOI
[36] - "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. | Zbl | DOI
[37] - "Green-Tao theorem in function fields", Acta Arith. 147 (2011), no. 2, p. 129-152. | Zbl | EuDML | DOI
[38] , & - "On sets of natural numbers whose difference set contains no squares", J. London Math. Soc. 37 (1988), no. 2, p. 219-231. | Zbl | DOI
[39] & - "Additive properties of dense subsets of sifted sequences", J. Théor. Nombres Bordeaux 13 (2001), no. 2, p. 559-581. | Zbl | EuDML | Numdam | DOI
[40] , , & - "Dense subsets of pseudorandom sets", in 49th Annual IEEE Symposium on Foundations of Computer Science (FOCS), Philadephia, 2008, p. 76-85.
[41] - "On certain sets of integers", J. London Math. Soc. 28 (1953), p. 104-109. | Zbl | DOI
[42] - "Generalized arithmetical progressions and sumsets", Acta Math. Hungar. 65 (1994), no. 4, p. 379-388. | Zbl | DOI
[43] - "On Roth's theorem on progressions", Ann. of Math. 174 (2011), no. 1, p. 619-636. | Zbl | DOI
[44] , "On the Bogolyubov-Ruzsa lemma", Anal. PDE 5 (2012), no. 3, p. 627-655. | Zbl | DOI
[45] - "On difference sets of sequences of integers. I", Acta Math. Acad. Sci. Hungar. 31 (1978), nos. 1-2, p. 125-149. | Zbl | DOI
[46] & - "Roth's theorem in many variables", preprint arXiv:1106.1601. | Zbl | DOI
[47] - "On sets of integers containing no elements in arithmetic progression", Acta Arith. 27 (1975), p. 199-245. | Zbl | EuDML | DOI
[48] - "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] , "A remark on Goldston-Yildirim correlation estimates", http://www.math.ucla.edu/~tao/preprints/Expository/gy-corr.dvi.
[50] & - "The primes contain arbitrarily long polynomial progressions", Acta Math. 201 (2008), no. 2, p. 213-305. | MR | Zbl | DOI
[51] , & - "Regularity, boosting, and efficiently simulating every high-entropy distribution", in 24th Annual IEEE Conference on Computational Complexity, Paris, 2009, p. 126-136. | MR
[52] - "On certain sets of positive density", J. London Math. Soc. 34 (1959), p. 358-360. | MR | Zbl | DOI
[53] - "Some theorems concerning the primes", Mat. Sbornik 2 (1937), p. 179-195. | Zbl | EuDML
[54] - "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. | MR | Zbl | DOI
[55] - "Universal characteristic factors and Furstenberg averages", J. Amer. Math. Soc. 20 (2007), no. 1, p. 53-97. | MR | Zbl | DOI






