Numbers with a large prime factor

Hong-Quan Liu; Jie Wu

Acta Arithmetica (1999)

  • Volume: 89, Issue: 2, page 163-187
  • ISSN: 0065-1036

How to cite

top

Hong-Quan Liu, and Jie Wu. "Numbers with a large prime factor." Acta Arithmetica 89.2 (1999): 163-187. <http://eudml.org/doc/207262>.

@article{Hong1999,
author = {Hong-Quan Liu, Jie Wu},
journal = {Acta Arithmetica},
keywords = {numbers with large prime factor; short interval; bilinear exponential sums; sieve methods; alternative sieve; greatest prime factor},
language = {eng},
number = {2},
pages = {163-187},
title = {Numbers with a large prime factor},
url = {http://eudml.org/doc/207262},
volume = {89},
year = {1999},
}

TY - JOUR
AU - Hong-Quan Liu
AU - Jie Wu
TI - Numbers with a large prime factor
JO - Acta Arithmetica
PY - 1999
VL - 89
IS - 2
SP - 163
EP - 187
LA - eng
KW - numbers with large prime factor; short interval; bilinear exponential sums; sieve methods; alternative sieve; greatest prime factor
UR - http://eudml.org/doc/207262
ER -

References

top
  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 and G. Harman, Numbers with a large prime factor, Acta Arith. 73 (1995), 119-145. 
  3. [3] R. C. Baker, G. Harman and J. Rivat, Primes of the form [ n c ] , J. Number Theory 50 (1995), 261-277. Zbl0822.11062
  4. [4] A. Balog, Numbers with a large prime factor I, Studia Sci. Math. Hungar. 15 (1980), 139-146; II, in: Topics in Classical Number Theory, Colloq. Math. Soc. János Bolyai 34, North-Holland, 1984, 49-67. Zbl0445.10033
  5. [5] A. Balog, G. Harman and J. Pintz, Numbers with a large prime factor IV, J. London Math. Soc. (2) 28 (1983), 218-226. Zbl0514.10034
  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] S. W. Graham, The greatest prime factor of the integers in an interval, J. London Math. Soc. (2) 24 (1981), 427-440. Zbl0442.10028
  9. [9] S. W. Graham and G. Kolesnik, Van der Corput's Method of Exponential Sums, Cambridge Univ. Press, 1991. Zbl0713.11001
  10. [10] G. Harman, On the distribution of αp modulo one, J. London Math. Soc. (2) 27 (1983), 9-13. Zbl0504.10018
  11. [11] D. R. Heath-Brown, The Pjateckiĭ-Šapiro prime number theorem, J. Number Theory 16 (1983), 242-266. Zbl0513.10042
  12. [12] D. R. Heath-Brown, The largest prime factor of the integers in an interval, Sci. China Ser. A 39 (1996), 449-476. Zbl0867.11064
  13. [13] D. R. Heath-Brown and C. H. Jia, The largest prime factor of the integers in an interval II, J. Reine Angew. Math. 498 (1998), 35-59. Zbl1066.11506
  14. [14] M. N. Huxley, Area, Lattice Points and Exponential Sums, Oxford Sci. Publ., Clarendon Press, Oxford, 1996. 
  15. [15] H. Iwaniec, A new form of the error term in the linear sieve, Acta Arith. 37 (1980), 307-320. Zbl0444.10038
  16. [16] C. H. Jia, The greatest prime factor of the integers in an interval I, Acta Math. Sinica 29 (1986), 815-825; II, Acta Math. Sinica 32 (1989), 188-199; III, Acta Math. Sinica (N.S.) 9 (1993), 321-336; IV, Acta Math. Sinica 12 (1996), 433-445. Zbl0621.10025
  17. [17] M. Jutila, On numbers with a large prime factor IV, J. Indian Math. Soc. (N.S.) 37 (1973), 43-53. 
  18. [18] H.-Q. Liu, The greatest prime factor of the integers in an interval, Acta Arith. 65 (1993), 301-328. Zbl0797.11071
  19. [19] H.-Q. Liu, A special triple exponential sum, Mathematika 42 (1995), 137-143. Zbl0829.11042
  20. [20] K. Ramachandra, A note on numbers with a large prime factor I, J. London Math. Soc. (2) 1 (1969), 303-306; II, J. Indian Math. Soc. 34 (1970), 39-48. Zbl0179.07301
  21. [21] E. C. Titchmarsh, The Theory of the Riemann Zeta-function, 2nd ed., revised by D. R. Heath-Brown, Clarendon Press, Oxford, 1986. Zbl0601.10026
  22. [22] J. Wu, Nombres 𝓑-libres dans les petits intervalles, Acta Arith. 65 (1993), 97-116. 

NotesEmbed ?

top

You must be logged in to post comments.