Integers with no large prime factors

Ti Zuo Xuan

Acta Arithmetica (1995)

  • Volume: 69, Issue: 4, page 303-327
  • ISSN: 0065-1036

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Ti Zuo Xuan. "Integers with no large prime factors." Acta Arithmetica 69.4 (1995): 303-327. <http://eudml.org/doc/206690>.

@article{TiZuoXuan1995,
author = {Ti Zuo Xuan},
journal = {Acta Arithmetica},
keywords = {integers free of large prime factors; asymptotic estimates; sieve methods},
language = {eng},
number = {4},
pages = {303-327},
title = {Integers with no large prime factors},
url = {http://eudml.org/doc/206690},
volume = {69},
year = {1995},
}

TY - JOUR
AU - Ti Zuo Xuan
TI - Integers with no large prime factors
JO - Acta Arithmetica
PY - 1995
VL - 69
IS - 4
SP - 303
EP - 327
LA - eng
KW - integers free of large prime factors; asymptotic estimates; sieve methods
UR - http://eudml.org/doc/206690
ER -

References

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  1. [1] N. G. de Bruijn, On the number of positive integers ≤x and free of prime factors >y, Nederl. Akad. Wetensch. Proc. Ser. A 54 (1951), 50-60. Zbl0042.04204
  2. [2] N. G. de Bruijn, The asymptotic behavior of a function occurring in the theory of primes, J. Indian Math. Soc. (N.S.) 15 (1951), 25-32. Zbl0043.06502
  3. [3] H. G. Diamond and H. Halberstam, The combinatorial sieve, in: Number Theory, Proc. 4th Matsci. Conf. Ootacamund/India 1984, Lecture Notes in Math. 1122, Springer, 1985, 63-73 
  4. [4] E. Fouvry et G. Tenenbaum, Entiers sans grand facteur premier en progressions arithmétiques, Proc. London Math. Soc. (3) 63 (1991), 449-494. Zbl0745.11042
  5. [5] H. Halberstam and H.-E. Richert, Sieve Methods, Academic Press, London, 1974. Zbl0298.10026
  6. [6] D. G. Hazlewood, Sums over positive integers with few prime factors, J. Number Theory 7 (1975), 189-207. Zbl0302.10037
  7. [7] A. Hildebrand, On the number of positive integers ≤x and free of prime factors >y, J. Number Theory 22 (1986), 289-307. Zbl0575.10038
  8. [8] A. Hildebrand and G. Tenenbaum, On integers free of large prime factors, Trans. Amer. Math. Soc. 296 (1986), 265-290. Zbl0601.10028
  9. [9] K. K. Norton, Numbers with small prime factors and the least k-th power non residue, Mem. Amer. Math. Soc. 106 (1971). Zbl0211.37801
  10. [10] H. E. Richert, Zur Abschätzung der Riemannschen Zetafunktion in der Nähe der Vertikalen σ = 1, Math. Ann. 169 (1967), 97-101. Zbl0161.04802
  11. [11] E. Saias, Sur le nombre des entiers sans grand facteur premier, J. Number Theory 32 (1989), 78-99. Zbl0676.10028
  12. [12] G. Tenenbaum, Cribler les entiers sans grand facteur premier, Philos. Trans. Roy. Soc. London Ser. A 345 (1993), 377-384. 
  13. [13] E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, 2nd ed. revised by D. R. Heath-Brown, Oxford, 1986. Zbl0601.10026
  14. [14] A. I. Vinogradov, On numbers with small prime divisors, Dokl. Akad. Nauk SSSR (N.S.) 109 (1956), 683-686 (in Russian). Zbl0071.27004

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