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ArticleOriginal scientific text

Title

Three additive cubic equations

Authors 1, 2, 1

Affiliations

  1. Department of Pure Mathematics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH, U.K.
  2. Mathematisches Institut, Bunsenstrasse 3-5, 3400 Göttingen, Federal Republic of Germany

Bibliography

  1. M. Aigner, Combinatorial Theory, Springer, Berlin 1979.
  2. R. C. Baker, Diagonal cubic equations II, Acta Arith. 53 (1989), 217-250.
  3. R. C. Baker and J. Brüdern, On pairs of additive cubic equations, J. Reine Angew. Math. 391 (1988), 157-180.
  4. B. J. Birch, Homogeneous forms of odd degree in a large number of variables, Mathematika 4 (1957), 102-105.
  5. R. Brauer, A note on systems of homogeneous algebraic equations, Bull. Amer. Math. Soc. 51 (1945), 749-755.
  6. J. Brüdern, On pairs of diagonal cubic forms, Proc. London Math. Soc. (3) 61 (1990), 273-343.
  7. J. Brüdern and R. J. Cook, On pairs of cubic diophantine inequalities, Mathematika, to appear.
  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.
  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.
  10. R. J. Cook, A note on a lemma of Hua, Quart. J. Math. Oxford Ser. 23 (1972), 287-288.
  11. R. J. Cook, Pairs of additive equations, Michigan Math. J. 19 (1972), 325-331.
  12. R. J. Cook, Pairs of additive congruences: cubic congruences, Mathematika 32 (1985), 286-300.
  13. R. J. Cook, Simultaneous additive congruences, Kon. Norske Vidensk. Selsk. Skr. 5 (1985), 1-7.
  14. H. Davenport and D. J. Lewis, Homogeneous additive equations, Proc. Roy. Soc. London A274 (1963), 443-460.
  15. H. Davenport and D. J. Lewis, Cubic equations of additive type, Philos. Trans. Roy. Soc. London A261 (1966), 97-136.
  16. H. Davenport and D. J. Lewis, Two additive equations, in: Proc. Sympos. Pure Math. 12, Amer. Math. Soc., 1967, 74-98.
  17. H. Davenport and D. J. Lewis, Simultaneous equations of additive type, Philos. Trans. Roy. Soc. London A264 (1969), 557-595.
  18. M. M. Dodson, Homogeneous additive congruences, Philos. Trans. Roy. Soc. London A261 (1966), 163-210.
  19. D. J. Lewis, Cubic congruences, Michigan Math. J. 4 (1957), 85-95.
  20. L. Low, J. Pitman and A. Wolff, Simultaneous additive congruences, J. Number Theory 29 (1988), 31-59.
  21. E. Stevenson, The Artin conjecture for three diagonal cubic forms, J. Number Theory 14 (1982), 374-390.
  22. R. C. Vaughan, On pairs of additive cubic equations, Proc. London Math. Soc. (3) 34 (1977), 354-364.
  23. R. C. Vaughan, The Hardy-Littlewood Method, University Press, Cambridge 1981.
  24. R. C. Vaughan, On Waring's problem for cubes, J. Reine Angew. Math. 365 (1986), 122-170.
  25. R. C. Vaughan, A new iterative method in Waring's problem, ActaMath. 162 (1989), 1-71.
Acta Arithmetica
1991-1992/60/1
Export to PBN, Opens in new tab
Pages:
29-83
Main language of publication
English
Received
1990-10-10
Published
1991
Exact and natural sciences