A sieve approach to the Waring-Goldbach problem, II On the seven cubes theorem

Jörg Brüdern

Acta Arithmetica (1995)

  • Volume: 72, Issue: 3, page 211-227
  • ISSN: 0065-1036

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Jörg Brüdern. "A sieve approach to the Waring-Goldbach problem, II On the seven cubes theorem." Acta Arithmetica 72.3 (1995): 211-227. <http://eudml.org/doc/206792>.

@article{JörgBrüdern1995,
author = {Jörg Brüdern},
journal = {Acta Arithmetica},
keywords = {number of representations; unrestricted Waring problem; circle method; weighted linear sieve},
language = {eng},
number = {3},
pages = {211-227},
title = {A sieve approach to the Waring-Goldbach problem, II On the seven cubes theorem},
url = {http://eudml.org/doc/206792},
volume = {72},
year = {1995},
}

TY - JOUR
AU - Jörg Brüdern
TI - A sieve approach to the Waring-Goldbach problem, II On the seven cubes theorem
JO - Acta Arithmetica
PY - 1995
VL - 72
IS - 3
SP - 211
EP - 227
LA - eng
KW - number of representations; unrestricted Waring problem; circle method; weighted linear sieve
UR - http://eudml.org/doc/206792
ER -

References

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  1. [1] J. Brüdern, On Waring's problem for fifth powers and some related topics, Proc. London Math. Soc. (3) 61 (1990), 457-479. Zbl0677.10036
  2. [2] J. Brüdern, Sieves, the circle method, and Waring's problem for cubes, Habilitationsschrift, Göttingen 1991; Mathematica Gottingensis 51 (1991). 
  3. [3] J. Brüdern, A note on cubic exponential sums, in: Séminaire de Théorie des Nombres, Paris 1990-91, S. David (ed.), Progr. Math. 108, Birkhäuser, Basel, 1992, 23-34. Zbl0815.11040
  4. [4] J. Brüdern, A sieve approach to the Waring-Goldbach problem I: Sums of four cubes, Ann. Sci. École Norm. Sup. Paris, to appear. Zbl0839.11045
  5. [5] J. Brüdern and E. Fouvry, Lagrange's four squares theorem with almost prime variables, J. Reine Angew. Math. 454 (1994), 59-96. Zbl0809.11060
  6. [6] G. Greaves, A weighted sieve of Brun's type, Acta Arith. 40 (1981), 297-332. Zbl0412.10033
  7. [7] L. K. Hua, Some results in additive prime number theory, Quart. J. Math. Oxford 9 (1938), 68-80. Zbl0018.29404
  8. [8] L. K. Hua, Additive Theory of Prime Numbers, Providence, R. I., 1965. Zbl0192.39304
  9. [9] R. C. Vaughan, The Hardy-Littlewood Method, Cambridge University Press, 1981. Zbl0455.10034
  10. [10] R. C. Vaughan, Some remarks on Weyl sums, in: Topics in Classical Number Theory, Colloq. Math. Soc. János Bolyai 34, North-Holland, Amsterdam, 1984. 
  11. [11] R. C. Vaughan, On Waring's problem for cubes, J. Reine Angew. Math. 365 (1986), 121-170. Zbl0574.10046
  12. [12] R. C. Vaughan, On Waring's problem for cubes II, J. London Math. Soc. (2) 39 (1989), 205-218. Zbl0677.10034
  13. [13] R. C. Vaughan, A new iterative method in Waring's problem, Acta Math. 162 (1989), 1-71. Zbl0665.10033
  14. [14] G. L. Watson, A proof of the seven cubes theorem, J. London Math. Soc. 26 (1951), 153-156. Zbl0042.04101
  15. [15] T. D. Wooley, Large improvements in Waring's problem, Ann. of Math. 135 (1992), 131-146 Zbl0754.11026

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