Editing Waring's problem (section)

==References==
*  G. I. Arkhipov, V. N. Chubarikov, [[Anatolii Alexeevitch Karatsuba|A. A. Karatsuba]], "Trigonometric sums in number theory and analysis". Berlin–New-York: Walter de Gruyter, (2004).
* G. I. Arkhipov, A. A. Karatsuba, V. N. Chubarikov, "Theory of multiple trigonometric sums". Moscow: Nauka, (1987).
* [[Yu. V. Linnik]], "An elementary solution of the problem of Waring by Schnirelman's method". ''Mat. Sb., N. Ser.'' '''12''' (54), 225–230 (1943).
* [[R. C. Vaughan]], "A new iterative method in Waring's problem". ''Acta Mathematica'' (162), 1–71 (1989).
* [[Ivan Matveyevich Vinogradov|I. M. Vinogradov]], "The method of trigonometrical sums in the theory of numbers". ''Trav. Inst. Math. Stekloff'' (23), 109 pp. (1947).
* I. M. Vinogradov, "On an upper bound for ''G''(''n'')". ''Izv. Akad. Nauk SSSR Ser. Mat.'' (23), 637–642 (1959).
* I. M. Vinogradov, A. A. Karatsuba, "The method of trigonometric sums in number theory", ''Proc. Steklov Inst. Math.'', 168, 3–30 (1986); translation from Trudy Mat. Inst. Steklova, 168, 4–30 (1984).
* {{cite journal | last1 = Ellison | first1 = W. J. | year = 1971 | title = Waring's problem | url = http://www.maa.org/programs/maa-awards/writing-awards/warings-problem| journal = American Mathematical Monthly | volume = 78 | issue = 1| pages = 10–36 | doi=10.2307/2317482| jstor = 2317482 }} Survey, contains the precise formula for ''G''(''k''), a simplified version of Hilbert's proof and a wealth of references.
* {{Cite book | author-link = Aleksandr Khinchin | last = Khinchin | first = A. Ya. | title = Three Pearls of Number Theory | publisher = Dover | location = Mineola, NY | year = 1998 | isbn = 978-0-486-40026-6 }} Has an elementary proof of the existence of ''G''(''k'') using [[Schnirelmann density]].
* {{cite book | first=Melvyn B. | last=Nathanson | title=Additive Number Theory: The Classical Bases | volume=164 | series=[[Graduate Texts in Mathematics]] | publisher=[[Springer-Verlag]] | year=1996 | isbn=0-387-94656-X | zbl=0859.11002 }} Has proofs of Lagrange's theorem, the [[polygonal number theorem]], Hilbert's proof of Waring's conjecture and the Hardy–Littlewood proof of the asymptotic formula for the number of ways to represent ''N'' as the sum of ''s'' ''k''th powers.
* [[Hans Rademacher]] and [[Otto Toeplitz]], ''The Enjoyment of Mathematics'' (1933) ({{isbn|0-691-02351-4}}). Has a proof of the Lagrange theorem, accessible to high-school students.