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Almost-primes represented by quadratic polynomials

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References

  1. Bateman, P.T., Horn, R.A.: A heuristic asymptotic formula concerning the distribution of prime numbers. Math. Comput.16, 363–367 (1962)

    Google Scholar 

  2. Buchstab, A.A.: Combinatorial intensification of the sieve method of Eratosthenes (in Russian). Uspehi Mat. Nauk22, no. 3 (135), 199–226 (1967)

    Google Scholar 

  3. Chen, J.-R.: On the distribution of almost-primes in an interval. Sci. Sinica18, 611–627 (1975)

    Google Scholar 

  4. Friedlander, J., Iwaniec, H.: Quadratic polynomials and quadratic forms, (to appear in Acta Math.),

  5. Halberstam, H., Richert, H.-E.: Almost-primes in short intervals and arithmetic progressions (unpublished),

  6. Hardy, G.H., Littlewood, J.E.: Some problems of Partitio Numerorum III. Acta Math.44, 1–70 (1923)

    Google Scholar 

  7. Hooley, C.: On the problem of divisors of quadratic polynomials. Acta Math.,110, 97–114 (1963)

    Google Scholar 

  8. Hooley, C.: On the greatest prime factor of a quadratic polynomial. Acta Math.117, 281–299 (1967)

    Google Scholar 

  9. Hooley, C.: On the Brun-Titchmarsh theorem. II. Proc. London Math. Soc.3 (30), 114–128 (1975)

    Google Scholar 

  10. Hooley, C.: On the Brun-Titchmarsh theorem. J. Reine Angew. Math.255, 60–79 (1972)

    Google Scholar 

  11. Iwaniec, H.: A new form of the error term in the linear sieve (to appear in Acta Arith.)

  12. Kuhn, P.: Neue Abschätzungen auf Grund der Viggo Brunschen Siebmethode, pp. 160–168, 12. Skand. Math. Kongr., Lund, 1953

  13. Kuhn, P.: Über die Primteiler eines Polynoms. Proc. Internat. Congress Math. Amsterdam,2, 35–37 (1954)

    Google Scholar 

  14. Levin, B.V.: A one-dimensional sieve (in Russian). Acta Arith.10, 387–397 (1964)

    Google Scholar 

  15. Motohashi, Y.: On some improvements of the Brun-Titchmarsh theorem, III. J. Math. Soc. Japan,27, 444–453 (1975)

    Google Scholar 

  16. Rademacher, H.: Beiträge zur Viggo Brunschen Methode in der Zahlentheorie. Abh. Math. Sem. Univ. Hamburg3, 12–30 (1924)

    Google Scholar 

  17. Ricci, G.: Su la congettura di Goldbach e la costante di Schnirelman. I. Ann. Scuola Norm. Sup. Pisa Sci. Fis. Math. (2),6, 91–116 (1937)

    Google Scholar 

  18. Richert, H.-E.: Selberg's sieve with weights. Mathematika16, 1–22 (1969)

    Google Scholar 

  19. Schinzel, A., Sierpiński, W.: Sur certaines hypothèses concernant les nombres premiers. Acta Arith.4, 185–208 (1958)

    Google Scholar 

  20. Smith, H.J.S.: Report on the theory of numbers. Collected mathematical papers. Vol. I, reprinted, Chelsea 1965,

  21. Wang, Y.: On sieve methods and some of their applications (in Chinese). Acta Math. Sinica9, 432–441 (1959)

    Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, Polish Academy of Sciences, PL-00-950, Warsaw, Poland

    Henryk Iwaniec

  2. Institut Mittag-Leffler, The Royal Swedish Academy of Sciences, S-18262, Djursholm, Sweden

    Henryk Iwaniec

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  1. Henryk Iwaniec
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Iwaniec, H. Almost-primes represented by quadratic polynomials. Invent Math 47, 171–188 (1978). https://doi.org/10.1007/BF01578070

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