PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
1992 | 62 | 2 | 125-149
Tytuł artykułu

On simultaneous diagonal equations and inequalities

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Czasopismo
Rocznik
Tom
62
Numer
2
Strony
125-149
Opis fizyczny
Daty
wydano
1992
otrzymano
1991-10-04
Twórcy
autor
  • Mathematisches Institut, Bunsenstrasse 3-5, 3400 Göttingen, Germany
autor
  • Department of Pure Mathematics, Hicks Building, Hounsfield Road, Sheffield S3 7RH, England
Bibliografia
  • [1] M. Aigner, Combinatorial Theory, Springer, Berlin 1979.
  • [2] O. D. Atkinson, J. Brüdern and R. J. Cook, Three additive cubic equations, Acta Arith. 60 (1991), 29-83.
  • [3] O. D. Atkinson, J. Brüdern and R. J. Cook, Simultaneous additive congruences to a large prime modulus, Mathematika, to appear.
  • [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.
  • [5] R. C. Baker, Diagonal cubic equations, II , Acta Arith. 53 (1989), 217-250.
  • [6] R. C. Baker, Diagonal cubic equations, III , Proc. London Math. Soc. (3) 58 (1989), 495-518.
  • [7] R. C. Baker and J. Brüdern, On pairs of additive cubic equations, J. Reine Angew. Math. 391 (1988), 157-180.
  • [8] B. J. Birch, Homogeneous forms of odd degree in a large number of variables, Mathematika 4 (1957), 102-105.
  • [9] J. Brüdern, Additive diophantine inequalities with mixed powers I, Mathematika 34 (1987), 124-130.
  • [10] J. Brüdern, Cubic diophantine inequalities, Mathematika 35 (1988), 51-58.
  • [11] J. Brüdern, On pairs of diagonal cubic forms, Proc. London Math. Soc. (3) 61 (1990), 273-343.
  • [12] J. Brüdern, On Waring's problem for fifth powers and some related topics, Proc. London Math. Soc. 457-479.
  • [13] J. Brüdernand R. J. Cook, On pairs of cubic diophantine inequalities, Mathematika 38 (1991), 250-263.
  • [14] J. Brüdernand R. J. Cook, Systems of cubic equations, in preparation.
  • [15] J. W. S. Cassels and M. J. T. Guy, On the Hasse principle for cubic surfaces, Mathematika 13 (1966), 111-120.
  • [16] R. J. Cook, Simultaneous quadratic equations, J. London Math. Soc. (2) 4 (1971), 319-326.
  • [17] R. J. Cook, A note on a lemma of Hua, Quart. J. Math. Oxford 23 (1972), 287-288.
  • [18] R. J. Cook, Pairs of additive equations, Michigan Math. J. 19 (1972), 325-331.
  • [19] R. J. Cook, Simultaneous quadratic equations II, Acta Arith. 25 (1973), 1-5.
  • [20] R. J. Cook, Simultaneous quadratic inequalities, Acta Arith. 25 (1974), 337-346.
  • [21] R. J. Cook, Pairs of additive equations II. Large odd degree, J. Number Theory 17 (1983), 80-92.
  • [22] R. J. Cook, Pairs of additive equations III: quintic equations, Proc. Edinburgh Math. Soc. (2) 26 (1983), 191-211.
  • [23] R. J. Cook, Pairs of additive equations IV. Sextic equations, Acta Arith. 43 (1984), 227-243.
  • [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.
  • [25] H. Davenport, Indefinite quadratic forms in many variables, Mathematika 3 (1956), 81-101.
  • [26] H. Davenport, Cubic forms in thirty-two variables, Philos. Trans. Roy. Soc. London Ser. A 251 (1959), 193-232.
  • [27] H. Davenport and D. J. Lewis, Homogeneous additive equations, Proc. Roy. Soc. London Ser. A 274 (1963), 443-460.
  • [28] H. Davenport and D. J. Lewis, Cubic equations of additive type, Philos. Trans. Roy. Soc. London Ser. A 261 (1966), 97-136.
  • [29] H. Davenport and D. J. Lewis, Simultaneous equations of additive type, Philos. Trans. Roy. Soc. London Ser. A 264 (1969), 557-595.
  • [30] H. Davenport and K. F. Roth, The solubility of certain Diophantine inequalities, Mathematika 2 (1955), 81-96.
  • [31] E. Dörner, Simultaneous diagonal equations over certain p-adic fields, J. Number Theory 36 (1990), 1-11.
  • [32] L. Low, J. Pitman and A. Wolff, Simultaneous diagonal congruences, J. Number Theory 29 (1988), 31-59.
  • [33] T. Nadesalingam, Diophantine inequalities in many variables, Ph.D. thesis, Univ. of Adelaide, South Australia, 1981.
  • [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.
  • [35] W. M. Schmidt, Linear forms with algebraic coefficients. I, J. Number Theory 3 (1971), 253-277.
  • [36] W. M. Schmidt, Diophantine inequalities for forms of odd degree, Adv. in Math. 38 (1980), 128-151.
  • [37] W. M. Schmidt, The solubility of certain p-adic equations, J. Number Theory 19 (1984), 63-80.
  • [38] R. C. Vaughan, On pairs of additive cubic equations, Proc. London Math. Soc. (3) 34 (1977), 354-364.
  • [39] R. C. Vaughan, The Hardy-Littlewood Method, Cambridge University Press, 1981.
  • [40] R. C. Vaughan, A new iterative method in Waring's problem, Acta Math. 162 (1989), 1-71.
  • [41] R. C. Vaughan and T. Wooley, On Waring's problem: some refinements, Proc. London Math. Soc. (3) 63 (1991), 35-68.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-aav62i2p125bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.