Duke Mathematical Journal

On Waring’s problem for four cubes

Jörg Brüdern and Nigel Watt

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Article information

Duke Math. J., Volume 77, Number 3 (1995), 583-606.

First available in Project Euclid: 20 February 2004

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11P05: Waring's problem and variants
Secondary: 11P55: Applications of the Hardy-Littlewood method [See also 11D85]


Brüdern, Jörg; Watt, Nigel. On Waring’s problem for four cubes. Duke Math. J. 77 (1995), no. 3, 583--606. doi:10.1215/S0012-7094-95-07718-7. https://projecteuclid.org/euclid.dmj/1077286534

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  • [1] J. Brüdern, Additive diophantine inequalities with mixed powers I, Mathematika 34 (1987), 124–130.
  • [2] J. Brüdern, A problem in additive number theory, Math. Proc. Cambridge Phil. Soc. 103 (1988), no. 1, 27–33.
  • [3] J. Brüdern, On Waring's problem for cubes, Math. Proc. Cambridge Phil. Soc. 109 (1991), no. 2, 229–256.
  • [4] J. Brüdern, Sieves, the circle method, and Waring's problem for cubes, Math. Gottingensis, vol. 51, Habilitationsschrift, Universität Göttingen, 1991.
  • [5] J. Brüdern, A note on cubic exponential sums, Seminaire de Theorie des nombres Paris 1990–1991 ed. S. David, Progress in Math., vol. 108, Birkhäuser, Basel, 1993, pp. 23–34.
  • [6] K. D. Boklan, A reduction technique in Waring's problem I, Acta Arith. 65 (1993), no. 2, 147–161.
  • [7] G. H. Hardy and J. E. Littlewood, Some problems of “Partitio Numerorum” I: A new solution of Waring's problem, Göttinger Nachrichten (1920), 33–54.
  • [8] R. R. Hall and G. Tenenbaum, Divisors, Cambridge Tracts in Mathematics, vol. 90, Cambridge University Press, Cambridge, 1988.
  • [9] C. Hooley, On the numbers that are representable as the sum of two cubes, J. Reine Angew. Math. 314 (1980), 146–173.
  • [10] H. Halberstam and H. E. Richert, Sieve Methods, Academic Press, London, 1974.
  • [11] R. C. Vaughan, The Hardy-Littlewood Method, Cambridge Tracts in Mathematics, vol. 80, Cambridge University Press, Cambridge, 1981.
  • [12] R. C. Vaughan, Some remarks on Weyl sums, Topics in Classical Number Theory (Budapest, 1981), Colloq. Math. Soc. Janos Bolyai, vol. 34, North-Holland, Amsterdam, 1984, pp. 1585–1602.
  • [13] R. C. Vaughan, Sums of three cubes, Bull. London Math. Soc. 17 (1985), no. 1, 17–20.
  • [14] R. C. Vaughan, On Waring's problem for cubes, J. Reine Angew. Math. 365 (1986), 122–170.
  • [15] R. C. Vaughan, On Waring's problem for cubes II, J. London Math. Soc. (2) 39 (1989), no. 2, 205–218.
  • [16] T. D. Wooley, Large improvements in Waring's problem, Ann. of Math. (2) 135 (1992), no. 1, 131–164.