@article{bwmeta1.element.bwnjournal-article-aav60i1p29bwm, author = {O. D. Atkinson and J. Br\"udern and R. J. Cook}, title = {Three additive cubic equations}, journal = {Acta Arithmetica}, volume = {58}, year = {1991}, pages = {29-83}, zbl = {0738.11027}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav60i1p29bwm} }
O. D. Atkinson; J. Brüdern; R. J. Cook. Three additive cubic equations. Acta Arithmetica, Tome 58 (1991) pp. 29-83. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav60i1p29bwm/
[000] [1] M. Aigner, Combinatorial Theory, Springer, Berlin 1979.
[001] [2] R. C. Baker, Diagonal cubic equations II, Acta Arith. 53 (1989), 217-250. | Zbl 0642.10041
[002] [3] R. C. Baker and J. Brüdern, On pairs of additive cubic equations, J. Reine Angew. Math. 391 (1988), 157-180. | Zbl 0642.10043
[003] [4] B. J. Birch, Homogeneous forms of odd degree in a large number of variables, Mathematika 4 (1957), 102-105. | Zbl 0081.04501
[004] [5] R. Brauer, A note on systems of homogeneous algebraic equations, Bull. Amer. Math. Soc. 51 (1945), 749-755. | Zbl 0063.00599
[005] [6] J. Brüdern, On pairs of diagonal cubic forms, Proc. London Math. Soc. (3) 61 (1990), 273-343. | Zbl 0709.11026
[006] [7] J. Brüdern and R. J. Cook, On pairs of cubic diophantine inequalities, Mathematika, to appear. | Zbl 0759.11009
[007] [8] N. G. de Bruijn, The asymptotic behaviour of a function occurring in the theory of primes, J. Indian Math. Soc. (N.S.) 15 (1951), 25-32. | Zbl 0043.06502
[008] [9] S. Chowla, H. B. Mann and E. G. Straus, Some applications of the Cauchy-Davenport theorem, Kon. Norske Vidensk. Selsk. Forh. 32 (1959), 74-80. | Zbl 0109.03206
[009] [10] R. J. Cook, A note on a lemma of Hua, Quart. J. Math. Oxford Ser. 23 (1972), 287-288. | Zbl 0238.10033
[010] [11] R. J. Cook, Pairs of additive equations, Michigan Math. J. 19 (1972), 325-331. | Zbl 0244.10046
[011] [12] R. J. Cook, Pairs of additive congruences: cubic congruences, Mathematika 32 (1985), 286-300. | Zbl 0586.10012
[012] [13] R. J. Cook, Simultaneous additive congruences, Kon. Norske Vidensk. Selsk. Skr. 5 (1985), 1-7.
[013] [14] H. Davenport and D. J. Lewis, Homogeneous additive equations, Proc. Roy. Soc. London A274 (1963), 443-460. | Zbl 0118.28002
[014] [15] H. Davenport and D. J. Lewis, Cubic equations of additive type, Philos. Trans. Roy. Soc. London A261 (1966), 97-136. | Zbl 0227.10038
[015] [16] H. Davenport and D. J. Lewis, Two additive equations, in: Proc. Sympos. Pure Math. 12, Amer. Math. Soc., 1967, 74-98.
[016] [17] H. Davenport and D. J. Lewis, Simultaneous equations of additive type, Philos. Trans. Roy. Soc. London A264 (1969), 557-595. | Zbl 0207.35304
[017] [18] M. M. Dodson, Homogeneous additive congruences, Philos. Trans. Roy. Soc. London A261 (1966), 163-210.
[018] [19] D. J. Lewis, Cubic congruences, Michigan Math. J. 4 (1957), 85-95. | Zbl 0077.05101
[019] [20] L. Low, J. Pitman and A. Wolff, Simultaneous additive congruences, J. Number Theory 29 (1988), 31-59. | Zbl 0643.10011
[020] [21] E. Stevenson, The Artin conjecture for three diagonal cubic forms, J. Number Theory 14 (1982), 374-390. | Zbl 0488.10022
[021] [22] R. C. Vaughan, On pairs of additive cubic equations, Proc. London Math. Soc. (3) 34 (1977), 354-364. | Zbl 0341.10044
[022] [23] R. C. Vaughan, The Hardy-Littlewood Method, University Press, Cambridge 1981. | Zbl 0455.10034
[023] [24] R. C. Vaughan, On Waring's problem for cubes, J. Reine Angew. Math. 365 (1986), 122-170. | Zbl 0574.10046
[024] [25] R. C. Vaughan, A new iterative method in Waring's problem, ActaMath. 162 (1989), 1-71. | Zbl 0665.10033