Hostname: page-component-77c89778f8-gq7q9 Total loading time: 0 Render date: 2024-07-17T11:45:22.168Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Waring-Siegel Theorem

Published online by Cambridge University Press:  20 November 2018

R. G. Ayoub
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The Waring problem deals with the decomposition of integers into sums of kth powers. Consider

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 5 , 1953 , pp. 439 - 450
Copyright
Copyright © Canadian Mathematical Society 1953

References

1. Hardy, G. H. and Littlewood, J. E., Some problems of partitio numerorum I: A new solution of Waring's Problem, Nachr. Ges. Wiss. Gottingen (1920), 33–54.Google Scholar
2. Hilbert, D., Beweis fur die Darstellbarkeit der ganzen Zahlen durch eine feste Anzahl nter Potenzen, Math. Ann., 67 (1909), 281–300.Google Scholar
3. Hua, L.-K., On a generalized Waring problem, Proc. London Math. Soc, 43 (1937), 161–182.Google Scholar
4. Hua, L.-K., On a generalized Waring problem, Chinese Math. Soc, 1 (1940), 23–61.Google Scholar
5. Hua, L.-K., Exponential sums over algebraic fields, Can. J. Math., 3 (1951), 44–51.Google Scholar
6. Hua, L.-K., On Waring's problem, Quarterly J. Math., 9 (1938), 199–201. Google Scholar
7. Landau, E., Über die Winogradoffsche Behandlung des Waringsche Problem, Math. Z., 31 (1930), 319–338.Google Scholar
8. Siegel, C. L., Additive Theorie der Zahlkörper, Math. Ann., 87 (1922), 1–35.Google Scholar
9. Siegel, C. L., Additive Theorie der Zahlkörper, Math. Ann., 88 (1923), 184–210.Google Scholar
10. Siegel, C. L., Generalization of Waring's problem to algebraic number fields, Amer. J. Math., 66 (1944), 122–136.Google Scholar
11. Siegel, C. L., Sums of mth powers of algebraic integers, Ann. Math., 46 (1945), 313–339.Google Scholar