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ArticleOriginal scientific text

Title

Numbers with a large prime factor

Authors 1, 2

Affiliations

  1. Department of Mathematics, Brigham Young University, Provo, Utah 84602, U.S.A.
  2. Mathematics Institute, University of Wales, Senghennydd Road, Cardiff CF2 4AG, U.K.

Bibliography

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  2. R. C. Baker, G. Harman and J. Rivat, Primes of the form [nc], J. Number Theory, to appear.
  3. E. Bombieri and H. Iwaniec, On the order of ζ(1/2 + it), Ann. Scuola Norm. Sup. Pisa 13 (1986), 449-472.
  4. A. Y. Cheer and D. A. Goldston, A differential delay equation arising from the sieve of Eratosthenes, Math. Comp. 55 (1990), 129-141.
  5. H. Davenport, Multiplicative Number Theory, 2nd ed. revised by H. L. Montgomery, Springer, New York, 1980.
  6. E. Fouvry, Sur le théorème de Brun-Titchmarsh, Acta Arith. 43 (1984), 417-424.
  7. E. Fouvry and H. Iwaniec, Exponential sums with monomials, J. Number Theory 33 (1989), 311-333.
  8. J. B. Friedlander, Integers free from large and small primes, Proc. London Math. Soc. 33 (1986), 565-576.
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  10. S. W. Graham and G. Kolesnik, Van der Corput's Method of Exponential Sums, Cambridge Univ. Press, 1991.
  11. G. Harman, On the distribution of αp modulo one, J. London Math. Soc. 27 (2) (1983), 9-13.
  12. C. H. Jia, The greatest prime factor of integers in short intervals II, Acta Math. Sinica 32 (1989), 188-199 (in Chinese).
  13. H.-Q. Liu, The greatest prime factor of the integers in an interval, Acta Arith. 65 (1993), 301-328.
  14. S. H. Min, Methods in Number Theory, Vol. 2, Science Press, 1983 (in Chinese).
  15. K. Ramachandra, A note on numbers with a large prime factor, J. London Math. Soc. 1 (2) (1969), 303-306.
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  17. E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, revised by D. R. Heath-Brown, Oxford University Press, 1986.
  18. I. M. Vinogradov, The Method of Trigonometrical Sums in the Theory of Numbers, translated and annotated by A. Davenport and K. F. Roth, Wiley, New York, 1954.
  19. N. Watt, Exponential sums and the Riemann zeta function II, J. London Math. Soc. 39 (1989), 385-404.
  20. J. Wu, P₂ dans les petits intervalles, in: Séminaire de Théorie des Nombres, Paris 1989-90, Birkhäuser, 1992, 233-267
Acta Arithmetica
1995/73/2
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Pages:
119-145
Main language of publication
English
Received
1994-08-01
Accepted
1995-02-21
Published
1995
Exact and natural sciences