Waring's problem with small prime factors

Gergely Harcos

Acta Arithmetica (1997)

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

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Gergely 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

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  1. [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. [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. [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. [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. [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. [6] A. Hildebrand and G. Tenenbaum, Integers without large prime factors, J. Théor. Nombres Bordeaux 5 (1993), 411-484. Zbl0797.11070
  7. [7] L.-K. Hua, Additive Primzahltheorie, Teubner, Leipzig, 1959; English transl.: Additive Theory of Prime Numbers, Amer. Math. Soc., Providence, 1965. 
  8. [8] R. C. Vaughan, The Hardy-Littlewood Method, Cambridge Tracts in Math. 80, Cambridge University Press, 1981. 
  9. [9] R. C. Vaughan, A new iterative method in Waring's problem, Acta Math. 162 (1989), 1-71. Zbl0665.10033
  10. [10] T. D. Wooley, Large improvements in Waring's problem, Ann. of Math. 135 (1992), 131-164. Zbl0754.11026

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