메뉴 건너뛰기




Volumn 43, Issue 1, 2006, Pages 3-23

The Green-Tao theorem on arithmetic progressions in the primes: An ergodic point of view

Author keywords

[No Author keywords available]

Indexed keywords


EID: 32044462762     PISSN: 02730979     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0273-0979-05-01086-4     Document Type: Conference Paper
Times cited : (18)

References (32)
  • 1
    • 0040207816 scopus 로고
    • The prime k-tuplets conjecture on average
    • Analytic number theory (Allerton Park, IL, 1989), Birkhäuser Boston. MR1084173 (92e:11105)
    • A. Balog. The prime k-tuplets conjecture on average. Analytic number theory (Allerton Park, IL, 1989), 47-75, Progr. Math., 85, Birkhäuser Boston, 1990. MR1084173 (92e:11105)
    • (1990) Progr. Math. , vol.85 , pp. 47-75
    • Balog, A.1
  • 2
    • 84971960652 scopus 로고
    • Linear equations in primes
    • MR1203292 (93m:11103)
    • A. Balog. Linear equations in primes. Mathematika, 39 (1992), 367-378. MR1203292 (93m:11103)
    • (1992) Mathematika , vol.39 , pp. 367-378
    • Balog, A.1
  • 3
    • 84974489786 scopus 로고
    • Weakly mixing PET
    • MR0912373 (89g:28022)
    • V. Bergelson. Weakly mixing PET. Erg. Th. & Dyn. Sys., 7 (1987), 337-349. MR0912373 (89g:28022)
    • (1987) Erg. Th. & Dyn. Sys. , vol.7 , pp. 337-349
    • Bergelson, V.1
  • 4
    • 0030554108 scopus 로고    scopus 로고
    • Polynomial extensions of van der Waerden's and Szemerédi's theorems
    • MR1325795 (96j:11013)
    • V. Bergelson and A. Leibman. Polynomial extensions of van der Waerden's and Szemerédi's theorems. J. Amer. Math. Soc., 9 (1996), 725-753. MR1325795 (96j:11013)
    • (1996) J. Amer. Math. Soc. , vol.9 , pp. 725-753
    • Bergelson, V.1    Leibman, A.2
  • 5
    • 0001232408 scopus 로고
    • Sur un théorème ergodique pour des mesures diagonales
    • MR0939438 (89e:22012)
    • J.-P. Conze and E. Lesigne. Sur un théorème ergodique pour des mesures diagonales. C. R. Acad. Sci. Paris, Série I, 306 (1988), 491-493. MR0939438 (89e:22012)
    • (1988) C. R. Acad. Sci. Paris, Série I , vol.306 , pp. 491-493
    • Conze, J.-P.1    Lesigne, E.2
  • 6
    • 84960611781 scopus 로고
    • On some sequences of integers
    • P. Erdös and P. Turán. On some sequences of integers. J. London Math. Soc., 11 (1936), 261-264.
    • (1936) J. London Math. Soc. , vol.11 , pp. 261-264
    • Erdös, P.1    Turán, P.2
  • 8
    • 51649169500 scopus 로고
    • Ergodic behavior of diagonal measures and a theorem of Szemerédi on arithmetic progressions
    • MR0498471 (58:16583)
    • H. Purstenberg. Ergodic behavior of diagonal measures and a theorem of Szemerédi on arithmetic progressions. J. d'Analyse Math., 31 (1977), 204-256. MR0498471 (58:16583)
    • (1977) J. D'Analyse Math. , vol.31 , pp. 204-256
    • Purstenberg, H.1
  • 9
    • 51249184670 scopus 로고
    • An ergodic Szemerédi theorem for commuting transformations
    • MR0531279 (82c:28032)
    • H. Furstenberg and Y. Katznelson. An ergodic Szemerédi theorem for commuting transformations. J. d'Analyse Math., 34 (1979), 275-291. MR0531279 (82c:28032)
    • (1979) J. D'Analyse Math. , vol.34 , pp. 275-291
    • Furstenberg, H.1    Katznelson, Y.2
  • 10
    • 0001951630 scopus 로고
    • A density version of the Hales-Jewett Theorem
    • MR1191743 (94f:28020)
    • H. Furstenberg and Y. Katznelson. A density version of the Hales-Jewett Theorem. J. d'Analyse Math., 57 (1991), 64-119. MR1191743 (94f:28020)
    • (1991) J. D'Analyse Math. , vol.57 , pp. 64-119
    • Furstenberg, H.1    Katznelson, Y.2
  • 11
    • 0002907973 scopus 로고    scopus 로고
    • n2 x)
    • Ohio State Univ. Math. Res. Inst. Publ., 5, Walter de Gruyter & Co, Berlin. MR1412607 (98e:28019)
    • n2 x). In Convergence in Ergodic Theory and Probability, Ohio State Univ. Math. Res. Inst. Publ., 5, Walter de Gruyter & Co, Berlin, 1996, 193-227. MR1412607 (98e:28019)
    • (1996) Convergence in Ergodic Theory and Probability , pp. 193-227
    • Furstenberg, H.1    Weiss, B.2
  • 13
    • 0035618488 scopus 로고    scopus 로고
    • A new proof of Szemerédi's Theorem
    • MR1844079 (2002k:11014)
    • T. Gowers. A new proof of Szemerédi's Theorem. GAFA, 11 (2001), 465-588. MR1844079 (2002k:11014)
    • (2001) GAFA , vol.11 , pp. 465-588
    • Gowers, T.1
  • 14
    • 32044453505 scopus 로고    scopus 로고
    • Personal communication
    • A. Granville. Personal communication.
    • Granville, A.1
  • 15
    • 85095800014 scopus 로고    scopus 로고
    • Roth's Theorem in the primes
    • To appear
    • B. Green. Roth's Theorem in the primes. To appear in Ann. Math.
    • Ann. Math.
    • Green, B.1
  • 16
    • 84871130932 scopus 로고    scopus 로고
    • The primes contain arbitrarily long arithmetic progressions
    • To appear
    • B. Green and T. Tao. The primes contain arbitrarily long arithmetic progressions. To appear, Ann. Math.
    • Ann. Math.
    • Green, B.1    Tao, T.2
  • 18
    • 33646862107 scopus 로고
    • Some problems of "partitio numerorum" III: On the expression of a number as a sum of primes
    • G. H. Hardy and J. E. Littlewood. Some problems of "partitio numerorum" III: on the expression of a number as a sum of primes. Acta Math., 44 (1923), 1-70.
    • (1923) Acta Math. , vol.44 , pp. 1-70
    • Hardy, G.H.1    Littlewood, J.E.2
  • 19
    • 84959787666 scopus 로고
    • Three primes and an almost prime in arithmetic progression
    • MR0616545 (82j:10074)
    • D. R. Heath-Brown. Three primes and an almost prime in arithmetic progression. J. London Math. Soc. (2), 23 (1981), 396-414. MR0616545 (82j:10074)
    • (1981) J. London Math. Soc. (2) , vol.23 , pp. 396-414
    • Heath-Brown, D.R.1
  • 20
    • 0039192901 scopus 로고    scopus 로고
    • Convergence of Conze-Lesigne averages
    • MR1827115 (2002d:28007)
    • B. Host and B. Kra. Convergence of Conze-Lesigne Averages. Erg. Th. & Dyn. Sys., 21 (2001), 493-509. MR1827115 (2002d:28007)
    • (2001) Erg. Th. & Dyn. Sys. , vol.21 , pp. 493-509
    • Host, B.1    Kra, B.2
  • 21
    • 23444458042 scopus 로고    scopus 로고
    • Nonconventional ergodic averages and nilmanifolds
    • B. Host and B. Kra. Nonconventional ergodic averages and nilmanifolds. Ann. Math., 161 (2005), 397-488.
    • (2005) Ann. Math. , vol.161 , pp. 397-488
    • Host, B.1    Kra, B.2
  • 22
    • 18444379725 scopus 로고    scopus 로고
    • Convergence of polynomial ergodic averages
    • B. Host and B. Kra. Convergence of polynomial ergodic averages. Israel J. Math., 149 (2005), 1-19.
    • (2005) Israel J. Math. , vol.149 , pp. 1-19
    • Host, B.1    Kra, B.2
  • 23
    • 18444400190 scopus 로고    scopus 로고
    • Convergence of multiple ergodic averages along polynomials of several variables
    • A. Leibman. Convergence of multiple ergodic averages along polynomials of several variables. Israel J. Math., 146 (2005), 303-316.
    • (2005) Israel J. Math. , vol.146 , pp. 303-316
    • Leibman, A.1
  • 24
    • 84941386622 scopus 로고
    • Ein Beitrag zur analytischen Zahlentheorie
    • F. Mertens. Ein Beitrag zur analytischen Zahlentheorie. Journal für Math., 78 (1874), 46-62.
    • (1874) Journal für Math. , vol.78 , pp. 46-62
    • Mertens, F.1
  • 25
    • 84968507672 scopus 로고
    • Twenty-two primes in arithmetic progression
    • MR1297475 (95j:11003)
    • A. Moran, P. Pritchard and A. Thyssen. Twenty-two primes in arithmetic progression. Math. Comp., 64 (1995), 1337-1339. MR1297475 (95j:11003)
    • (1995) Math. Comp. , vol.64 , pp. 1337-1339
    • Moran, A.1    Pritchard, P.2    Thyssen, A.3
  • 26
    • 16244382826 scopus 로고
    • The general sieve method and its place in prime number theory
    • Cambridge MR0044563 (13:438d)
    • A. Selberg. The general sieve method and its place in prime number theory. Proc. ICM, vol. 1, Cambridge (1950), 286-292. MR0044563 (13:438d)
    • (1950) Proc. ICM , vol.1 , pp. 286-292
    • Selberg, A.1
  • 27
    • 0001549458 scopus 로고
    • On sets of integers containing no k elements in arithmetic progression
    • MR0369312 (51:5547)
    • E. Szemerédi. On sets of integers containing no k elements in arithmetic progression. Acta Arith., 27 (1975), 199-245. MR0369312 (51:5547)
    • (1975) Acta Arith. , vol.27 , pp. 199-245
    • Szemerédi, E.1
  • 30
    • 0002996391 scopus 로고
    • Über Summen von Primzahlen und Primzahlquadraten
    • J. G. van der Corput. Über Summen von Primzahlen und Primzahlquadraten. Math. Ann., 116 (1939), 1-50.
    • (1939) Math. Ann. , vol.116 , pp. 1-50
    • Van Der Corput, J.G.1
  • 31
    • 0000590051 scopus 로고
    • Beweis einer Baudetschen Vermutung
    • B. L. van der Waerden. Beweis einer Baudetschen Vermutung. Nieuw Arch. Wisk., 15 (1927), 212-216.
    • (1927) Nieuw Arch. Wisk. , vol.15 , pp. 212-216
    • Van Der Waerden, B.L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.