Limitation to the asymptotic formula in Waring's problem

• Autorzy: W. K. A. Loh
• Języki publikacji: EN

Kategorie tematyczne

• 11P05: Waring's problem and variants

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1996
• Tom: 74
• Numer: 1
• Strony: 1-15

Daty

wydano

1996

otrzymano

1994-04-15

poprawiono

1994-11-15

Twórcy

autor

W. K. A. Loh

• Department of Mathematics, Imperial College, Huxley Building, 180 Queen's Gate London SW7 2BZ, U.K.
• Department of Applied Mathematics, Hong Kong Polytechnics University, Hung Hom, Hong Kong

Bibliografia

• [1] K. D. Boklan, The asymptotic formula in Waring's Problem, Mathematika 41 (1994), 329-347.
• [2] G. H. Hardy, On the representation of a number as the sum of any number of squares, and in particular of five, Trans. Amer. Math. Soc. 21 (1920), 255-284.
• [3] G. H. Hardy and J. E. Littlewood, Some problems of 'Partitio Numerorum', IV, Math. Z. 12 (1922), 161-188.
• [4] D. R. Heath-Brown, Weyl's inequality, Hua's inequality, and Waring's problem, J. London Math. Soc. 38 (1988), 216-230.
• [5] L. K. Hua, On Waring's problem, Quart. J. Math. Oxford 9 (1938), 199-202.
• [6] L. K. Hua, An improvement of Vinogradov's mean-value theorem and several applications, Quart. J. Math. Oxford 20 (1949), 48-61.
• [7] H. L. Montgomery and R. C. Vaughan, Error terms in additive prime number theory, Quart. J. Math. Oxford 24 (1973), 207-216.
• [8] R. C. Vaughan, On the addition of sequences of integers, J. Number Theory 4 (1972), 1-16.
• [9] R. C. Vaughan, The Hardy-Littlewood Method, Cambridge University Press, 1981.
• [10] R. C. Vaughan, On Waring's problem for cubes, J. Reine Angew. Math. 365 (1986), 122-170.
• [11] R. C. Vaughan, On Waring's problem for smaller exponent II, Mathematika 33 (1986), 6-22.
• [12] I. M. Vinogradov, New estimates for Weyl's sum, Dokl. Akad. Nauk SSSR 8 (1935), 195-198.
• [13] T. D. Wooley, On Vinogradov's mean value theorem, Mathematika 39 (1992), 379-399.