ArticleOriginal scientific text

Title

Sums of fifth powers and related topics

Authors 1, 2

Affiliations

  1. Department of Mathematics, Faculty of Education, Iwate University, Morioka, 020-8550 Japan
  2. Department of Mathematics, University of Michigan, East Hall, 525, East University Avenue, Ann Arbor, Michigan 48109-1109, U.S.A.

Keywords

sums of fifth powers, quintic polynomials, Waring's problem

Bibliography

  1. J. Brüdern, On Waring's problem for fifth powers and some related topics, Proc. London Math. Soc. (3) 61 (1990), 457-479.
  2. T. Estermann, Einige Sätze über quadratfrei Zahlen, Math. Ann. 105 (1931), 653-662.
  3. L.-K. Hua, On a generalized Waring problem. II, J. Chinese Math. Soc. 2 (1940), 175-191.
  4. K. Kawada and T. D. Wooley, Sums of fourth powers and related topics, J. Reine Angew. Math., to appear.
  5. W. M. Schmidt, Equations over Finite Fields. An Elementary Approach, Lecture Notes in Math. 536, Springer, Berlin, 1976.
  6. K. Thanigasalam, Improvement on Davenport's iterative method and new results in additive number theory. III, Acta Arith. 48 (1987), 97-116.
  7. R. C. Vaughan, On Waring's problem for smaller exponents, Proc. London Math. Soc. (3) 52 (1986), 445-463.
  8. R. C. Vaughan, A new iterative method in Waring's Problem, Acta Math. 162 (1989), 1-71.
  9. R. C. Vaughan, The Hardy-Littlewood Method, 2nd ed., Cambridge Univ. Press, 1997.
  10. R. C. Vaughan and T. D. Wooley, On Waring's Problem: some refinements, Proc. London Math. Soc. (3) 63 (1991), 35-68.
  11. R. C. Vaughan and T. D. Wooley, Further improvements in Waring's Problem, Acta Math. 174 (1995), 147-240.
  12. T. D. Wooley, Large improvements in Waring's problem, Ann. of Math. 135 (1992), 131-164.
  13. H. B. Yu, On Waring's problem with polynomial summands, Acta Arith. 76 (1996), 131-144.
Pages:
27-65
Main language of publication
English
Received
1998-01-27
Accepted
1998-08-12
Published
1998
Exact and natural sciences