The greatest prime factor of the integers in an interval

Hong-Quan Liu

Acta Arithmetica (1993)

  • Volume: 65, Issue: 4, page 301-328
  • ISSN: 0065-1036

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Hong-Quan Liu. "The greatest prime factor of the integers in an interval." Acta Arithmetica 65.4 (1993): 301-328. <http://eudml.org/doc/206583>.

@article{Hong1993,
author = {Hong-Quan Liu},
journal = {Acta Arithmetica},
keywords = {largest prime divisor},
language = {eng},
number = {4},
pages = {301-328},
title = {The greatest prime factor of the integers in an interval},
url = {http://eudml.org/doc/206583},
volume = {65},
year = {1993},
}

TY - JOUR
AU - Hong-Quan Liu
TI - The greatest prime factor of the integers in an interval
JO - Acta Arithmetica
PY - 1993
VL - 65
IS - 4
SP - 301
EP - 328
LA - eng
KW - largest prime divisor
UR - http://eudml.org/doc/206583
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] E. Bombieri and H. Iwaniec, On the order of ζ(1/2+it), Ann. Scuola Norm. Sup. Pisa 13 (1986), 449-472. Zbl0615.10047
  3. [3] E. Fouvry and H. Iwaniec, Exponential sums with monomials, J. Number Theory 33 (1989), 311-333. Zbl0687.10028
  4. [4] S. W. Graham, The greatest prime factor of the integers in an interval, J. London Math. Soc. 24 (1981), 427-440. Zbl0442.10028
  5. [5] D. R. Heath-Brown, Prime numbers in short intervals and a generalized Vaughan identity, Canad. J. Math. 34 (1982), 1365-1377. Zbl0478.10024
  6. [6] H. Iwaniec, A new form of the error term in the linear sieve, Acta Arith. 37 (1980), 307-320. Zbl0444.10038
  7. [7] C. H. Jia, The greatest prime factor of the integers in an interval (II), Acta Math. Sinica (Chinese) 32 (1989), 188-199. Cf. also doctoral thesis, Peking University, 1987. Zbl0672.10030
  8. [8] A. A. Karatsuba, Principles of Analytic Number Theory, Nauka, 1975 (in Russian). 
  9. [9] H. Liu, On square-full numbers in short intervals, Acta Math. Sinica (N.S.) 6 (1990), 148-164. Zbl0708.11044
  10. [10] S. H. Min, Methods in Number Theory, Vol. 2, Science Press, 1981 (in Chinese). Zbl0649.10001
  11. [11] K. Ramachandra, A note on numbers with a large prime factor, J. London Math. Soc. 1 (1969), 303-306. Zbl0179.07301
  12. [12] K. Ramachandra, A note on numbers with a large prime factor (II), J. Indian Math. Soc. 34 (1970), 39-48. Zbl0218.10057

Citations in EuDML Documents

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  1. R. C. Baker, G. Harman, Numbers with a large prime factor
  2. Roger C. Baker, Glyn Harman, Sparsely totient numbers
  3. Hong-Quan Liu, The distribution of 4-full numbers
  4. Hong-Quan Liu, Divisor problems of 4 and 3 dimensions
  5. Hong-Quan Liu, Jie Wu, Numbers with a large prime factor
  6. Hong-Quan Liu, On some divisor problems
  7. Hong-Quan Liu, On a fundamental result in van der Corput's method of estimating exponential sums
  8. J. Wu, On the average number of unitary factors of finite abelian groups

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