Acta Mathematica

, Volume 156, Issue 1, pp 203–251 | Cite as

Primes in arithmetic progressions to large moduli

  • E. Bombieri
  • J. B. Friedlander
  • H. Iwaniec
Article

Keywords

Arithmetic Progression Dispersion Method Implied Constant Divisor Problem Large Modulus 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Bombieri, E., On the large sieve.Mathematika, 12 (1965), 201–225.CrossRefMATHMathSciNetGoogle Scholar
  2. [2]
    Deshouillers J.-M. &Ivaniec, H., Kloosterman sums and Fourier coefficients of cusp forms.Invent. Math., 70 (1982), 219–288.CrossRefMATHMathSciNetGoogle Scholar
  3. [3]
    Elliott, P. D. T. A. &Halberstam, H., A conjecture in prime number theory.Symp. Math., 4 (INDAM Rome, 1968–69), 59–72.Google Scholar
  4. [4]
    Fouvry, E., Répartition des suites dans les progressions arithmétiques.Acta Arith. 41 (1982), 359–382.MATHMathSciNetGoogle Scholar
  5. [5]
    —, Autour du théorème de Bombieri-Vinogradov.Acta Math., 152 (1984), 219–244.CrossRefMATHMathSciNetGoogle Scholar
  6. [6]
    Fouvry, E. &Iwaniec, H., On a theorem of Bombieri-Vinogradov type.Mathematika, 27 (1980), 135–172.CrossRefMATHMathSciNetGoogle Scholar
  7. [7]
    — Primes in arithmetic progressions.Acta Arith., 42 (1983), 197–218.MATHMathSciNetGoogle Scholar
  8. [8]
    Friedlander, J. &Iwaniec, H., On Bombieri's asymptotic sieve.Ann. Scuola Norm. Sup. Pisa Cl. Sci (4), 5 (1978), 719–756.MATHMathSciNetGoogle Scholar
  9. [9]
    — Incomplete Kloosterman sums and a divisor problem.Ann. Math., 121 (1985), 319–350.CrossRefMATHGoogle Scholar
  10. [10]
    Friedlander, J. The divisor problem for arithmetic progressions. To appear inActa Arith.Google Scholar
  11. [11]
    Gallagher, P. X., Bombieri's mean value theorem.Mathematika, 14 (1967), 14–20.CrossRefMATHMathSciNetGoogle Scholar
  12. [12]
    Heath-Brown, D. R., Prime numbers in short intervals and a generalized Vaughan identity.Canad. J. Math., 34 (1982), 1365–1377.CrossRefMATHMathSciNetGoogle Scholar
  13. [13]
    Hooley, C., On the Barban-Davenport-Halberstam Theorem III.J. London Math. Soc. (2), 10 (1975), 249–256.CrossRefMATHMathSciNetGoogle Scholar
  14. [14]
    Iwaniec, H., The half dimensional sieve.Acta Arith., 29 (1976), 67–95.MathSciNetGoogle Scholar
  15. [15]
    —, A new form of the error term in the linear sieve.Acta Arith., 37 (1980), 307–320.MATHMathSciNetGoogle Scholar
  16. [16]
    Linnik, Ju. V., All large numbers are sums of a prime and two squares (a problem of Hardy and Littlewood), II.Mat. Sb. 53 (1961), 3–38;Amer. Math. Soc. Transl., 37 (1964), 197–240.MathSciNetGoogle Scholar
  17. [17]
    —,The dispersion method in binary additive problems. Amer. Math. Soc., Providence, 1963.MATHGoogle Scholar
  18. [18]
    Motohashi, Y., An induction principle for the generalization of Bombieri's Prime Number Theorem.Proc. Japan Acad., 52 (1976), 273–275.CrossRefMATHMathSciNetGoogle Scholar
  19. [19]
    Shiu, P., A Brun-Titchmarsh theorem for multiplicative functions.J. Reine Angew. Math., 313 (1980), 161–170.MATHMathSciNetGoogle Scholar
  20. [20]
    Vaughan, R. C., An elementary method in prime number theory.Acta Arith., 37 (1980), 111–115.MATHMathSciNetGoogle Scholar
  21. [21]
    Vinogradov, A. I., On the density hypothesis for DirichletL-functions.Izv. Akad. Nauk SSSR Ser. Math., 29 (1965), 903–934; correctionibid. Izv. Akad. Nauk SSSR Ser. Math., 30 (1966), 719–720.MATHGoogle Scholar
  22. [22]
    Wolke, D., Über mittlere Verteilung der Werte zahlentheoretischer Funktionen auf Restklassen I.Math. Ann., 202 (1973), 1–25; IIibid. Math. Ann., 204 (1973), 145–153.CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Almqvist & Wiksell 1986

Authors and Affiliations

  • E. Bombieri
    • 1
  • J. B. Friedlander
    • 1
  • H. Iwaniec
    • 1
  1. 1.Institute for Advanced StudyPrincetonUSA

Personalised recommendations