Comptes Rendus
Number Theory
Sums of distinct integral squares in real quadratic fields
Comptes Rendus. Mathématique, Volume 349 (2011) no. 9-10, pp. 497-500.

We show that the elements of the ring of integers of real quadratic fields which are sums of integral squares are in fact sums of distinct squares, provided their norm is large enough.

Nous montrons que les entiers totalement positifs de normes suffisamment grandes sont des sommes de carrés distincts dans lʼanneau des entiers des corps réel quadratique.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2011.03.019
Byeong Moon Kim 1; Poo-Sung Park 2

1 Department of Mathematics, Gangnung-Wonju National University, Gangneung Daehangno 120, Gangneung City, Gangwon Province, 210-702, Republic of Korea
2 Department of Mathematics Education, Kyungnam University, Changwon, 631-701, Republic of Korea
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Byeong Moon Kim; Poo-Sung Park. Sums of distinct integral squares in real quadratic fields. Comptes Rendus. Mathématique, Volume 349 (2011) no. 9-10, pp. 497-500. doi : 10.1016/j.crma.2011.03.019. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.03.019/

[1] H. Cohn Calculation of class numbers by decomposition into three integral squares in the field of 21/2 and 31/2, Amer. J. Math., Volume 83 (1961), pp. 33-56

[2] H. Cohn; G. Pall Sums of four squares in a quadratic ring, Trans. Amer. Math. Soc., Volume 105 (1962), pp. 536-556

[3] F. Götzky Über eine zahlentheoretische Anwendung von Modulfunktionen zweier Veränderlicher, Math. Ann., Volume 100 (1928) no. 1, pp. 411-437

[4] J.Y. Kim, Y.M. Lee, Sums of distinct integral squares in Q(2), Q(3) and Q(6), preprint.

[5] L. Mordell On the representation of a binary quadratic form as a sum of squares of linear forms, Math. Z., Volume 35 (1932) no. 1, pp. 1-15

[6] P.-S. Park Sums of distinct integral squares in Q(5), C. R. Acad. Sci. Paris, Sér. I, Volume 346 (2008) no. 13–14, pp. 723-725

[7] R. Scharlau, Zur Darstellbarkeit von totalreellen ganzen algebraischen Zahlen durch Summen von Quadraten, Dissertation, Bielefeld, 1979.

[8] R. Sprague Über Zerlegungen in ungleiche Quadratzahlen, Math. Z., Volume 51 (1948), pp. 289-290

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