Hostname: page-component-8448b6f56d-c4f8m Total loading time: 0 Render date: 2024-04-25T02:34:44.090Z Has data issue: false hasContentIssue false
  • English
  • Français

SUMS OF DISTINCT INTEGRAL SQUARES IN , AND

Part of: Forms and linear algebraic groups

Published online by Cambridge University Press:  08 September 2011

JI YOUNG KIM  and
YOUNG MIN LEE
JI YOUNG KIM*
Affiliation:
Department of Mathematical Sciences, Seoul National University, Gwanakro 599, Gwanak-gu, Seoul, 151-747, Korea (email: jykim98@snu.ac.kr)
YOUNG MIN LEE
Affiliation:
Department of Mathematical Sciences, Seoul National University, Gwanakro 599, Gwanak-gu, Seoul, 151-747, Korea (email: younglee@snu.ac.kr)
*
✉For correspondence; e-mail: jykim98@snu.ac.kr
Rights & Permissions [Opens in a new window]

Abstract

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.

In this article, we determine all the totally positive integers of which can be represented as sums of distinct integral squares, where m=2, 3, 6.

Keywords

totally positive integersum of distinct squares

MSC classification

Secondary: 11E25: Sums of squares and representations by other particular quadratic forms
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 85 , Issue 1 , February 2012 , pp. 1 - 10
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

Footnotes

The first named author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010-0023321).

References

[1]Cohn, H., ‘Numerical study of the representation of a totally positive quadratic integer as the sum of quadratic integral squares’, Numer. Math. 1 (1959), 121–134.CrossRefGoogle Scholar
[2]Cohn, H., ‘Decomposition into four integral squares in the fields of 21/2 and 31/2’, Amer. J. Math. 82 (1960), 301–322.CrossRefGoogle Scholar
[3]Cohn, H., ‘Calculation of class numbers by decomposition into three integral squares in the field of 21/2 and 31/2’, Amer. J. Math. 83 (1961), 33–56.CrossRefGoogle Scholar
[4]Cohn, H. and Pall, G., ‘Sums of four squares in a quadratic ring’, Trans. Amer. Math. Soc. 105 (1962), 536–556.CrossRefGoogle Scholar
[5]Götzky, F., ‘Über eine zahlentheoretische Anwendung von Modulfunktionen zweier Veränderlichen’, Math. Ann. 100 (1928), 411–437.CrossRefGoogle Scholar
[6]Kim, B. M., ‘On nonvanishing sum of integral squares of ’, Preprint.Google Scholar
[7]Lagrange, J. L., Démonstration d’un théorème d’arithmétique, Nouveaux Mém. Acad. Roy. Sci. Belles-Lettres, Berlin, 1770; reprinted in Œuvres de Lagrange, 3 (1869), 189–201.Google Scholar
[8]Maass, H., ‘Über die Darstellung total positiver Zahlen des Körpers als Summe von drei Quadraten’, Abh. Math. Semin. Hansischen Univ. 14 (1941), 185–191.CrossRefGoogle Scholar
[9]Park, P.-S., ‘Sums of distinct integral squares in ’, C. R. Math. Acad. Sci. Paris 346 (2008), 723–725.CrossRefGoogle Scholar
[10]Scharlau, R., ‘Zur Darstellbarkeit von totalreellen ganzen algebraischen Zahlen durch Summen von Quadraten’, PhD Thesis, Universität Bielefeld, 1979.Google Scholar
[11]Siegel, C. L., ‘Sums of mth powers of algebraic integers’, Ann. of Math. (2) 46 (1945), 313–339.CrossRefGoogle Scholar
[12]Sprague, R., ‘Über Zerlegungen in ungleiche Quadratzahlen’, Math. Z. 51 (1948), 289–290.CrossRefGoogle Scholar