Numbers with a large prime factor

R. C. Baker; G. Harman

Acta Arithmetica (1995)

  • Volume: 73, Issue: 2, page 119-145
  • ISSN: 0065-1036

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R. C. Baker, and G. Harman. "Numbers with a large prime factor." Acta Arithmetica 73.2 (1995): 119-145. <http://eudml.org/doc/206814>.

@article{R1995,
author = {R. C. Baker, G. Harman},
journal = {Acta Arithmetica},
keywords = {greatest prime factor; sieve methods; bilinear sums},
language = {eng},
number = {2},
pages = {119-145},
title = {Numbers with a large prime factor},
url = {http://eudml.org/doc/206814},
volume = {73},
year = {1995},
}

TY - JOUR
AU - R. C. Baker
AU - G. Harman
TI - Numbers with a large prime factor
JO - Acta Arithmetica
PY - 1995
VL - 73
IS - 2
SP - 119
EP - 145
LA - eng
KW - greatest prime factor; sieve methods; bilinear sums
UR - http://eudml.org/doc/206814
ER -

References

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  1. [1] R. C. Baker, The greatest prime factor of the integers in an interval, Acta Arith. 47 (1986), 193-231. Zbl0553.10035
  2. [2] R. C. Baker, G. Harman and J. Rivat, Primes of the form [ n c ] , J. Number Theory, to appear. 
  3. [3] E. Bombieri and H. Iwaniec, On the order of ζ(1/2 + it), Ann. Scuola Norm. Sup. Pisa 13 (1986), 449-472. Zbl0615.10047
  4. [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. [5] H. Davenport, Multiplicative Number Theory, 2nd ed. revised by H. L. Montgomery, Springer, New York, 1980. Zbl0453.10002
  6. [6] E. Fouvry, Sur le théorème de Brun-Titchmarsh, Acta Arith. 43 (1984), 417-424. 
  7. [7] E. Fouvry and H. Iwaniec, Exponential sums with monomials, J. Number Theory 33 (1989), 311-333. Zbl0687.10028
  8. [8] J. B. Friedlander, Integers free from large and small primes, Proc. London Math. Soc. 33 (1986), 565-576. Zbl0344.10021
  9. [9] S. W. Graham, The greatest prime factor of the integers in an interval, J. London Math. Soc. 24 (1981), 427-440. Zbl0442.10028
  10. [10] S. W. Graham and G. Kolesnik, Van der Corput's Method of Exponential Sums, Cambridge Univ. Press, 1991. Zbl0713.11001
  11. [11] G. Harman, On the distribution of αp modulo one, J. London Math. Soc. 27 (2) (1983), 9-13. Zbl0504.10018
  12. [12] C. H. Jia, The greatest prime factor of integers in short intervals II, Acta Math. Sinica 32 (1989), 188-199 (in Chinese). Zbl0672.10030
  13. [13] H.-Q. Liu, The greatest prime factor of the integers in an interval, Acta Arith. 65 (1993), 301-328. Zbl0797.11071
  14. [14] S. H. Min, Methods in Number Theory, Vol. 2, Science Press, 1983 (in Chinese). 
  15. [15] K. Ramachandra, A note on numbers with a large prime factor, J. London Math. Soc. 1 (2) (1969), 303-306. Zbl0179.07301
  16. [16] K. Ramachandra, A note on numbers with a large prime factor, II, J. Indian Math. Soc. 34 (1970), 39-48. Zbl0218.10057
  17. [17] E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, revised by D. R. Heath-Brown, Oxford University Press, 1986. Zbl0601.10026
  18. [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. Zbl0055.27504
  19. [19] N. Watt, Exponential sums and the Riemann zeta function II, J. London Math. Soc. 39 (1989), 385-404. Zbl0678.10027
  20. [20] J. Wu, P₂ dans les petits intervalles, in: Séminaire de Théorie des Nombres, Paris 1989-90, Birkhäuser, 1992, 233-267 

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