# The greatest prime factor of the integers in an interval

Acta Arithmetica (1993)

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

## Access Full Article

top## How to cite

topHong-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

top- [1] R. C. Baker, The greatest prime factor of the integers in an interval, Acta Arith. 47 (1986), 193-231. Zbl0553.10035
- [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] E. Fouvry and H. Iwaniec, Exponential sums with monomials, J. Number Theory 33 (1989), 311-333. Zbl0687.10028
- [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] D. R. Heath-Brown, Prime numbers in short intervals and a generalized Vaughan identity, Canad. J. Math. 34 (1982), 1365-1377. Zbl0478.10024
- [6] H. Iwaniec, A new form of the error term in the linear sieve, Acta Arith. 37 (1980), 307-320. Zbl0444.10038
- [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] A. A. Karatsuba, Principles of Analytic Number Theory, Nauka, 1975 (in Russian).
- [9] H. Liu, On square-full numbers in short intervals, Acta Math. Sinica (N.S.) 6 (1990), 148-164. Zbl0708.11044
- [10] S. H. Min, Methods in Number Theory, Vol. 2, Science Press, 1981 (in Chinese). Zbl0649.10001
- [11] K. Ramachandra, A note on numbers with a large prime factor, J. London Math. Soc. 1 (1969), 303-306. Zbl0179.07301
- [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

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

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.