Additive representation in thin sequences, I : Waring's problem for cubes
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 34 (2001) no. 4, pp. 471-501.
@article{ASENS_2001_4_34_4_471_0,
author = {Br\"udern, J\"org and Kawada, Koichi and Wooley, Trevor D},
title = {Additive representation in thin sequences, {I} : {Waring's} problem for cubes},
journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
pages = {471--501},
publisher = {Elsevier},
volume = {Ser. 4, 34},
number = {4},
year = {2001},
doi = {10.1016/s0012-9593(01)01067-9},
zbl = {1020.11062},
mrnumber = {1852007},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/s0012-9593(01)01067-9/}
}
TY  - JOUR
AU  - Brüdern, Jörg
AU  - Wooley, Trevor D
TI  - Additive representation in thin sequences, I : Waring's problem for cubes
JO  - Annales scientifiques de l'École Normale Supérieure
PY  - 2001
DA  - 2001///
SP  - 471
EP  - 501
VL  - Ser. 4, 34
IS  - 4
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/s0012-9593(01)01067-9/
UR  - https://zbmath.org/?q=an%3A1020.11062
UR  - https://www.ams.org/mathscinet-getitem?mr=1852007
UR  - https://doi.org/10.1016/s0012-9593(01)01067-9
DO  - 10.1016/s0012-9593(01)01067-9
LA  - en
ID  - ASENS_2001_4_34_4_471_0
ER  - 
%0 Journal Article
%A Brüdern, Jörg
%A Wooley, Trevor D
%T Additive representation in thin sequences, I : Waring's problem for cubes
%J Annales scientifiques de l'École Normale Supérieure
%D 2001
%P 471-501
%V Ser. 4, 34
%N 4
%I Elsevier
%U https://doi.org/10.1016/s0012-9593(01)01067-9
%R 10.1016/s0012-9593(01)01067-9
%G en
%F ASENS_2001_4_34_4_471_0
Brüdern, Jörg; Kawada, Koichi; Wooley, Trevor D. Additive representation in thin sequences, I : Waring's problem for cubes. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 34 (2001) no. 4, pp. 471-501. doi : 10.1016/s0012-9593(01)01067-9. http://archive.numdam.org/articles/10.1016/s0012-9593(01)01067-9/

[1] Brüdern J, A problem in additive number theory, Math. Proc. Cambridge Philos. Soc. 103 (1988) 27-33. | MR | Zbl

[2] Brüdern J, On Waring's problem for cubes, Math. Proc. Cambridge Philos. Soc. 109 (1991) 229-256. | MR | Zbl

[3] Brüdern J., Kawada K., Wooley T.D., Additive representation in thin sequences, II: the binary Goldbach problem, Mathematika, to appear. | MR | Zbl

[4] Brüdern J., Kawada K., Wooley T.D., Additive representation in thin sequences, III: asymptotic formulae, Acta Arith., to appear. | MR | Zbl

[5] Brüdern J., Kawada K., Wooley T.D., Additive representation in thin sequences, IV: lower bound methods, Quart. J. Math. Oxford, to appear. | MR | Zbl

[6] Brüdern J., Kawada K., Wooley T.D., Additive representation in thin sequences, V: mixed problems of Waring's type, Math. Scand., to appear. | MR | Zbl

[7] Brüdern J, Watt N, On Waring's problem for four cubes, Duke Math. J. 77 (1995) 583-606. | MR | Zbl

[8] Davenport H, On Waring's problem for cubes, Acta Math. 71 (1939) 123-143. | JFM | MR

[9] Davenport H, Analytic Methods for Diophantine Equations and Diophantine Inequalities, Ann Arbor Publishers, Ann Arbor, 1962. | MR | Zbl

[10] Estermann T, Einige Sätze über quadratfreie Zahlen, Math. Ann. 105 (1931) 653-662. | JFM | MR

[11] Hardy G.H, Littlewood J.E, Some problems of “Partitio Numerorum”. I, A new solution of Waring's problem, Göttinger Nachrichten (1920) 33-54. | JFM

[12] Kawada K, On the sum of four cubes, Mathematika 43 (1996) 323-348. | MR | Zbl

[13] Linnik J.V, On the representation of large numbers as sums of seven cubes, Mat. Sbornik 12 (1943) 218-224. | MR | Zbl

[14] Vaughan R.C, On Waring's problem for cubes, J. Reine Angew. Math. 365 (1986) 122-170. | MR | Zbl

[15] Vaughan R.C, A new iterative method in Waring's problem, Acta Math. 162 (1989) 1-71. | MR | Zbl

[16] Vaughan R.C, On Waring's problem for cubes II, J. London Math. Soc. 39 (2) (1989) 205-218. | MR | Zbl

[17] Vaughan R.C, The Hardy-Littlewood Method, Cambridge University Press, Cambridge, 1997. | Zbl

[18] Vaughan R.C, Wooley T.D, On Waring's problem: some refinements, Proc. London Math. Soc. 63 (3) (1991) 35-68. | MR | Zbl

[19] Watson G.L, A proof of the seven cube theorem, J. London Math. Soc. 26 (1951) 153-156. | MR | Zbl

[20] Wooley T.D, On simultaneous additive equations, II, J. Reine Angew. Math. 419 (1991) 141-198. | MR | Zbl

[21] Wooley T.D, Large improvements in Waring's problem, Ann. of Math. 135 (2) (1992) 131-164. | MR | Zbl

[22] Wooley T.D, Breaking classical convexity in Waring's problem: sums of cubes and quasi-diagonal behaviour, Invent. Math. 122 (1995) 421-451. | MR | Zbl

Cited by Sources: