Duke Mathematical Journal

On Waring’s problem for four cubes

Jörg Brüdern and Nigel Watt
Source: Duke Math. J. Volume 77, Number 3 (1995), 583-606.
First Page: Show Hide
Primary Subjects: 11P05
Secondary Subjects: 11P55
Full-text: Access denied (no subscription detected)
We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.
If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077286534
Mathematical Reviews number (MathSciNet): MR1324635
Zentralblatt MATH identifier: 0828.11051
Digital Object Identifier: doi:10.1215/S0012-7094-95-07718-7

References

[1] J. Brüdern, Additive diophantine inequalities with mixed powers I, Mathematika 34 (1987), 124–130.
Zentralblatt MATH: 0642.10044
[2] J. Brüdern, A problem in additive number theory, Math. Proc. Cambridge Phil. Soc. 103 (1988), no. 1, 27–33.
Mathematical Reviews (MathSciNet): MR89c:11150
Zentralblatt MATH: 0655.10041
Digital Object Identifier: doi:10.1017/S0305004100064586
[3] J. Brüdern, On Waring's problem for cubes, Math. Proc. Cambridge Phil. Soc. 109 (1991), no. 2, 229–256.
Mathematical Reviews (MathSciNet): MR91m:11081
Zentralblatt MATH: 0729.11046
Digital Object Identifier: doi:10.1017/S0305004100069711
[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.
Mathematical Reviews (MathSciNet): MR95e:11107
Zentralblatt MATH: 0815.11040
[6] K. D. Boklan, A reduction technique in Waring's problem I, Acta Arith. 65 (1993), no. 2, 147–161.
Mathematical Reviews (MathSciNet): MR95b:11094
Zentralblatt MATH: 0785.11049
[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.
Zentralblatt MATH: 47.0114.02
[8] R. R. Hall and G. Tenenbaum, Divisors, Cambridge Tracts in Mathematics, vol. 90, Cambridge University Press, Cambridge, 1988.
Mathematical Reviews (MathSciNet): MR90a:11107
Zentralblatt MATH: 0653.10001
[9] C. Hooley, On the numbers that are representable as the sum of two cubes, J. Reine Angew. Math. 314 (1980), 146–173.
Mathematical Reviews (MathSciNet): MR81d:10036
Zentralblatt MATH: 0423.10026
Digital Object Identifier: doi:10.1515/crll.1980.314.146
[10] H. Halberstam and H. E. Richert, Sieve Methods, Academic Press, London, 1974.
Mathematical Reviews (MathSciNet): MR54:12689
Zentralblatt MATH: 0298.10026
[11] R. C. Vaughan, The Hardy-Littlewood Method, Cambridge Tracts in Mathematics, vol. 80, Cambridge University Press, Cambridge, 1981.
Mathematical Reviews (MathSciNet): MR84b:10002
Zentralblatt MATH: 0455.10034
[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.
Mathematical Reviews (MathSciNet): MR86e:11067
Zentralblatt MATH: 0545.10024
[13] R. C. Vaughan, Sums of three cubes, Bull. London Math. Soc. 17 (1985), no. 1, 17–20.
Mathematical Reviews (MathSciNet): MR86j:11103
Zentralblatt MATH: 0562.10022
Digital Object Identifier: doi:10.1112/blms/17.1.17
[14] R. C. Vaughan, On Waring's problem for cubes, J. Reine Angew. Math. 365 (1986), 122–170.
Mathematical Reviews (MathSciNet): MR87j:11103
Zentralblatt MATH: 0574.10046
Digital Object Identifier: doi:10.1515/crll.1986.365.122
[15] R. C. Vaughan, On Waring's problem for cubes II, J. London Math. Soc. (2) 39 (1989), no. 2, 205–218.
Mathematical Reviews (MathSciNet): MR90c:11073
Zentralblatt MATH: 0677.10034
Digital Object Identifier: doi:10.1112/jlms/s2-39.2.205
[16] T. D. Wooley, Large improvements in Waring's problem, Ann. of Math. (2) 135 (1992), no. 1, 131–164.
Mathematical Reviews (MathSciNet): MR93b:11129
Zentralblatt MATH: 0754.11026
Digital Object Identifier: doi:10.2307/2946566

2012 © Duke University Press

Duke Mathematical Journal

Duke Mathematical Journal

Turn MathJax Off
What is MathJax?