@article{bwmeta1.element.bwnjournal-article-aav62i2p125bwm,
author = {J. Br\"udern and R. J. Cook},
title = {On simultaneous diagonal equations and inequalities},
journal = {Acta Arithmetica},
volume = {62},
year = {1992},
pages = {125-149},
zbl = {0774.11015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav62i2p125bwm}
}
J. Brüdern; R. J. Cook. On simultaneous diagonal equations and inequalities. Acta Arithmetica, Tome 62 (1992) pp. 125-149. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav62i2p125bwm/
[000] [1] M. Aigner, Combinatorial Theory, Springer, Berlin 1979.
[001] [2] O. D. Atkinson, J. Brüdern and R. J. Cook, Three additive cubic equations, Acta Arith. 60 (1991), 29-83. | Zbl 0738.11027
[002] [3] O. D. Atkinson, J. Brüdern and R. J. Cook, Simultaneous additive congruences to a large prime modulus, Mathematika, to appear. | Zbl 0774.11016
[003] [4] R. C. Baker, Diagonal cubic equations, I , in: Théorie des Nombres, Number Theory, J.-M. De Koninck and C. Levesque (eds.), de Gruyter, Berlin 1989, 15-28.
[004] [5] R. C. Baker, Diagonal cubic equations, II , Acta Arith. 53 (1989), 217-250. | Zbl 0642.10041
[005] [6] R. C. Baker, Diagonal cubic equations, III , Proc. London Math. Soc. (3) 58 (1989), 495-518. | Zbl 0642.10042
[006] [7] R. C. Baker and J. Brüdern, On pairs of additive cubic equations, J. Reine Angew. Math. 391 (1988), 157-180. | Zbl 0642.10043
[007] [8] B. J. Birch, Homogeneous forms of odd degree in a large number of variables, Mathematika 4 (1957), 102-105. | Zbl 0081.04501
[008] [9] J. Brüdern, Additive diophantine inequalities with mixed powers I, Mathematika 34 (1987), 124-130. | Zbl 0642.10044
[009] [10] J. Brüdern, Cubic diophantine inequalities, Mathematika 35 (1988), 51-58. | Zbl 0659.10015
[010] [11] J. Brüdern, On pairs of diagonal cubic forms, Proc. London Math. Soc. (3) 61 (1990), 273-343. | Zbl 0709.11026
[011] [12] J. Brüdern, On Waring's problem for fifth powers and some related topics, Proc. London Math. Soc. 457-479. | Zbl 0677.10036
[012] [13] J. Brüdernand R. J. Cook, On pairs of cubic diophantine inequalities, Mathematika 38 (1991), 250-263. | Zbl 0759.11009
[013] [14] J. Brüdernand R. J. Cook, Systems of cubic equations, in preparation.
[014] [15] J. W. S. Cassels and M. J. T. Guy, On the Hasse principle for cubic surfaces, Mathematika 13 (1966), 111-120. | Zbl 0151.03405
[015] [16] R. J. Cook, Simultaneous quadratic equations, J. London Math. Soc. (2) 4 (1971), 319-326. | Zbl 0224.10021
[016] [17] R. J. Cook, A note on a lemma of Hua, Quart. J. Math. Oxford 23 (1972), 287-288. | Zbl 0238.10033
[017] [18] R. J. Cook, Pairs of additive equations, Michigan Math. J. 19 (1972), 325-331. | Zbl 0244.10046
[018] [19] R. J. Cook, Simultaneous quadratic equations II, Acta Arith. 25 (1973), 1-5.
[019] [20] R. J. Cook, Simultaneous quadratic inequalities, Acta Arith. 25 (1974), 337-346. | Zbl 0278.10021
[020] [21] R. J. Cook, Pairs of additive equations II. Large odd degree, J. Number Theory 17 (1983), 80-92. | Zbl 0516.10043
[021] [22] R. J. Cook, Pairs of additive equations III: quintic equations, Proc. Edinburgh Math. Soc. (2) 26 (1983), 191-211. | Zbl 0497.10036
[022] [23] R. J. Cook, Pairs of additive equations IV. Sextic equations, Acta Arith. 43 (1984), 227-243. | Zbl 0532.10008
[023] [24] R. J. Cook, Pairs of additive congruences: quintic congruences II, in: Computers in Mathematical Research, N. M. Stephens and M. P. Thorne (eds.), Clarendon Press, Oxford 1988, 93-117. | Zbl 0637.10014
[024] [25] H. Davenport, Indefinite quadratic forms in many variables, Mathematika 3 (1956), 81-101. | Zbl 0072.27205
[025] [26] H. Davenport, Cubic forms in thirty-two variables, Philos. Trans. Roy. Soc. London Ser. A 251 (1959), 193-232. | Zbl 0084.27202
[026] [27] H. Davenport and D. J. Lewis, Homogeneous additive equations, Proc. Roy. Soc. London Ser. A 274 (1963), 443-460. | Zbl 0118.28002
[027] [28] H. Davenport and D. J. Lewis, Cubic equations of additive type, Philos. Trans. Roy. Soc. London Ser. A 261 (1966), 97-136. | Zbl 0227.10038
[028] [29] H. Davenport and D. J. Lewis, Simultaneous equations of additive type, Philos. Trans. Roy. Soc. London Ser. A 264 (1969), 557-595. | Zbl 0207.35304
[029] [30] H. Davenport and K. F. Roth, The solubility of certain Diophantine inequalities, Mathematika 2 (1955), 81-96. | Zbl 0066.29301
[030] [31] E. Dörner, Simultaneous diagonal equations over certain p-adic fields, J. Number Theory 36 (1990), 1-11. | Zbl 0709.11027
[031] [32] L. Low, J. Pitman and A. Wolff, Simultaneous diagonal congruences, J. Number Theory 29 (1988), 31-59. | Zbl 0643.10011
[032] [33] T. Nadesalingam, Diophantine inequalities in many variables, Ph.D. thesis, Univ. of Adelaide, South Australia, 1981.
[033] [34] J. Pitman, Pairs of diagonal inequalities, in: Recent Progress in Analytic Number Theory, Vol. 2, H. Halberstam and C. Hooley (eds.), Academic Press, London 1981, 183-215.
[034] [35] W. M. Schmidt, Linear forms with algebraic coefficients. I, J. Number Theory 3 (1971), 253-277. | Zbl 0221.10034
[035] [36] W. M. Schmidt, Diophantine inequalities for forms of odd degree, Adv. in Math. 38 (1980), 128-151. | Zbl 0448.10019
[036] [37] W. M. Schmidt, The solubility of certain p-adic equations, J. Number Theory 19 (1984), 63-80. | Zbl 0541.10024
[037] [38] R. C. Vaughan, On pairs of additive cubic equations, Proc. London Math. Soc. (3) 34 (1977), 354-364. | Zbl 0341.10044
[038] [39] R. C. Vaughan, The Hardy-Littlewood Method, Cambridge University Press, 1981. | Zbl 0455.10034
[039] [40] R. C. Vaughan, A new iterative method in Waring's problem, Acta Math. 162 (1989), 1-71. | Zbl 0665.10033
[040] [41] R. C. Vaughan and T. Wooley, On Waring's problem: some refinements, Proc. London Math. Soc. (3) 63 (1991), 35-68. | Zbl 0736.11058