# Waring's problem with small prime factors

Acta Arithmetica (1997)

- Volume: 80, Issue: 2, page 165-185
- ISSN: 0065-1036

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top## How to cite

topGergely Harcos. "Waring's problem with small prime factors." Acta Arithmetica 80.2 (1997): 165-185. <http://eudml.org/doc/207035>.

@article{GergelyHarcos1997,

author = {Gergely Harcos},

journal = {Acta Arithmetica},

keywords = {smooth numbers; estimate for divisor function; Hardy-Littlewood circle method; variant of Waring's problem},

language = {eng},

number = {2},

pages = {165-185},

title = {Waring's problem with small prime factors},

url = {http://eudml.org/doc/207035},

volume = {80},

year = {1997},

}

TY - JOUR

AU - Gergely Harcos

TI - Waring's problem with small prime factors

JO - Acta Arithmetica

PY - 1997

VL - 80

IS - 2

SP - 165

EP - 185

LA - eng

KW - smooth numbers; estimate for divisor function; Hardy-Littlewood circle method; variant of Waring's problem

UR - http://eudml.org/doc/207035

ER -

## References

top- [1] A. Balog and A. Sárközy, On sums of integers having small prime factors I, Studia Sci. Math. Hungar. 19 (1984), 35-47. Zbl0569.10025
- [2] J. Brüdern, A sieve approach to the Waring-Goldbach problem II. On the seven cubes theorem, Acta Arith. 72 (1995), 211-227. Zbl0839.11046
- [3] J. Brüdern and E. Fouvry, Lagrange's four squares theorem with almost prime variables, J. Reine Angew. Math. 454 (1994), 59-96. Zbl0809.11060
- [4] 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; II, ibid. 69 (1966), 239-247. Zbl0042.04204
- [5] A. Hildebrand, On the number of positive integers ≤ x and free of prime factors > y, J. Number Theory 22 (1986), 289-307. Zbl0575.10038
- [6] A. Hildebrand and G. Tenenbaum, Integers without large prime factors, J. Théor. Nombres Bordeaux 5 (1993), 411-484. Zbl0797.11070
- [7] L.-K. Hua, Additive Primzahltheorie, Teubner, Leipzig, 1959; English transl.: Additive Theory of Prime Numbers, Amer. Math. Soc., Providence, 1965.
- [8] R. C. Vaughan, The Hardy-Littlewood Method, Cambridge Tracts in Math. 80, Cambridge University Press, 1981.
- [9] R. C. Vaughan, A new iterative method in Waring's problem, Acta Math. 162 (1989), 1-71. Zbl0665.10033
- [10] T. D. Wooley, Large improvements in Waring's problem, Ann. of Math. 135 (1992), 131-164. Zbl0754.11026

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