Sums of fifth powers and related topics

• Autorzy: Koichi Kawada , Trevor D. Wooley
• Języki publikacji: EN

Słowa kluczowe

EN

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

Kategorie tematyczne

• 11P05: Waring's problem and variants
• 11P55: Applications of the Hardy-Littlewood method

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1998-1999
• Tom: 87
• Numer: 1
• Strony: 27-65

Daty

wydano

1998

otrzymano

1998-01-27

poprawiono

1998-08-12

Twórcy

autor

Koichi Kawada

• Department of Mathematics, Faculty of Education, Iwate University, Morioka, 020-8550 Japan

autor

Trevor D. Wooley

• Department of Mathematics, University of Michigan, East Hall, 525, East University Avenue, Ann Arbor, Michigan 48109-1109, U.S.A.

Bibliografia

• [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.