The representation of almost all numbers as sums of unlike powers
Journal de théorie des nombres de Bordeaux, Tome 13 (2001) no. 1, pp. 227-240.

Nous prouvons dans cet article que presque tout entier s'écrit comme la somme d'un cube, d'un bicarré, ..., et d'une puissance dixième.

We prove in this article that almost all large integers have a representation as the sum of a cube, a biquadrate, ..., and a tenth power.

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Laporta, M. B. S.; Wooley, T. D. The representation of almost all numbers as sums of unlike powers. Journal de théorie des nombres de Bordeaux, Tome 13 (2001) no. 1, pp. 227-240. http://www.numdam.org/item/JTNB_2001__13_1_227_0/

[1] J. Brüdern, Sums of squares and higher powers. II. J. London Math. Soc. (2) 35 (1987), 244-250. | MR | Zbl

[2] J. Brüdern, A problem in additive number theory. Math. Proc. Cambridge Philos. Soc. 103 (1988), 27-33. | MR | Zbl

[3] J. Brüdern, T.D. Wooley, On Waring's problem: two cubes and seven biquadrates. Tsukuba Math. J. 24 (2000), 387-417. | MR | Zbl

[4] H. Davenport, H. Heilbronn, On Waring's problem: two cubes and one square. Proc. London Math. Soc. (2) 43 (1937), 73-104. | JFM | Zbl

[5] K.B. Ford, The representation of numbers as sums of unlike powers. J. London Math. Soc. (2) 51 (1995), 14-26. | MR | Zbl

[6] K.B. Ford, The representation of numbers as sums of unlike powers. II. J. Amer. Math. Soc. 9 (1996), 919-940. | MR | Zbl

[7] C. Hooley, On a new approach to various problems of Waring's type. In: Recent progress in analytic number theory, vol. 1 (Durham, 1979), Academic Press, London (1981), 127-191. | MR | Zbl

[8] K.F. Roth, Proof that almost all positive integers are sums of a square, a positive cube and a fourth power. J. London Math. Soc. 24 (1949), 4-13. | MR | Zbl

[9] K.F. Roth, A problem in additive number theory. Proc. London Math. Soc. (2) 53 (1951), 381-395. | MR | Zbl

[10] K. Thanigasalam, On additive number theory. Acta Arith. 13 (1967/68), 237-258. | EuDML | MR | Zbl

[11] K. Thanigasalam, On sums of powers and a related problem. Acta Arith. 36 (1980), 125-141. | EuDML | MR | Zbl

[12] K. Thanigasalam, On certain additive representations of integers. Portugal. Math. 42 (1983/84), 447-465. | EuDML | MR | Zbl

[13] R.C. Vaughan, On the representation of numbers as sums of powers of natural numbers. Proc. London Math. Soc. (3) 21 (1970), 160-180. | MR | Zbl

[14] R.C. Vaughan, On sums of mixed powers. J. London Math. Soc. (2) 3 (1971), 677-688. | MR | Zbl

[15] R.C. Vaughan, A ternary additive problem. Proc. London Math. Soc. (3) 41 (1980), 516-532. | MR | Zbl

[16] R.C. Vaughan, On Waring's problem for cubes. J. Reine Angew. Math. 365 (1986), 122-170. | EuDML | MR | Zbl

[17] R.C. Vaughan, On Waring's problem for smaller exponents. Proc. London Math. Soc. (3) 52 (1986), 445-463. | MR | Zbl

[18] R.C. Vaughan, A new iterative method in Waring's problem. Acta Math. 162 (1989), 1-71. | MR | Zbl

[19] R.C. Vaughan, The Hardy-Littlewood method. Cambridge Tract No. 125, 2nd Edition, Cambridge University Press, 1997. | MR | Zbl

[20] R.C. Vaughan, T.D. Wooley, On Waring's problem: some refinements. Proc. London Math. Soc. (3) 63 (1991), 35-68. | MR | Zbl

[21] R.C. Vaughan, T.D. Wooley, Further improvements in Waring's problem. Acta Math. 174 (1995), 147-240. | MR | Zbl

[22] R.C. Vaughan, T.D. Wooley, Further improvements in Waring's problem, IV: higher powers. Acta Arith. 94 (2000), 203-285. | EuDML | MR | Zbl

[23] T.D. Wooley, On simultaneous additive equations, II. J. Reine Angew. Math. 419 (1991), 141-198. | EuDML | MR | Zbl

[24] T.D. Wooley, Large improvements in Waring's problem. Ann. of Math. (2) 135 (1992), 131-164. | MR | Zbl

[25] T.D. Wooley, New estimates for smooth Weyl sums. J. London Math. Soc. (2) 51 (1995), 1-13. | MR | Zbl

[26] T.D. Wooley, Breaking classical convexity in Waring's problem: sums of cubes and quasi-diagonal behaviour. Invent. Math. 122 (1995), 421-451. | EuDML | MR | Zbl