Waring ’ s Problem : A Survey

@inproceedings{Vaughan2002WaringS,
  title={Waring ’ s Problem : A Survey},
  author={R. C. Vaughan and Trevor D. Wooley},
  year={2002}
}
It is presumed that by this, in modern notation, Waring meant that for every k ≥ 3 there are numbers s such that every natural number is the sum of at most s k-th powers of natural numbers and that the smallest such number g(k) satisfies g(3) = 9, g(4) = 19. By the end of the nineteenth century, the existence of g(k) was known for only a finite number of values of k. There is an account of this work in Dickson [48], and as far as we have been able to ascertain, by 1909 its existence was known… CONTINUE READING
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References

Publications referenced by this paper.
Showing 1-10 of 59 references

On a new approach to various problems of Waring’s type

  • C. Hooley
  • Recent progress in analytic number theory, Vol. 1
  • 1979
Highly Influential
8 Excerpts

Sur les sommes de puissances entières

  • H. Davenport
  • C. R. Acad. Sci. Paris, Sér. A 207
  • 1938
Highly Influential
14 Excerpts

A new estimate for G(n) in Waring’s problem

  • I. M. Vinogradov
  • Dokl. Akad. Nauk SSSR 5
  • 1934
Highly Influential
9 Excerpts

Le problème de Waring pour l’anneau des polynômes sur un corps fini

  • M. Car
  • Séminaire de Téorie des Nombres 1972–1973 (Univ…
  • 1973
Highly Influential
4 Excerpts

Dartsellung total positiver Zahlen durch Quadrate

  • C. L. Siegel
  • Math. Z. 11
  • 1921
Highly Influential
5 Excerpts

Über die Gleichverteilung von Zahlen mod Eins

  • H. Weyl
  • Math. Ann. 77
  • 1916
Highly Influential
6 Excerpts

Sums of squares

  • W. C. Jagy, I. Kaplansky
  • cubes, and higher powers, Experiment. Math. 4
  • 1995
Highly Influential
2 Excerpts

Fractional parts of powers of rational numbers

  • M. A. Bennett
  • Math. Proc. Cambridge Philos. Soc. 114
  • 1993
Highly Influential
3 Excerpts

A lower bound on the value ‖(3/2)

  • A. K. Dubitskas
  • Uspekhi Mat. Nauk 45 (1990), 153–154, translation…
  • 1990
Highly Influential
2 Excerpts

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