Limitation to the asymptotic formula in Waring's problem

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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

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