Comptes Rendus
no. 13-14
Number Theory
Sums of distinct integral squares in Q(5)

Presented by: Jean-Pierre Serre

Poo-Sung Park1
1 School of Computational Sciences, Korea Institute for Advanced Study, Hoegiro 87, Dongdaemun-gu, Seoul, 130-722, Korea
Comptes Rendus. Mathématique, Volume 346 (2008) no. 13-14, pp. 723-725.

In this Note, we determine all the totally positive integers of Q(5) which cannot be represented as sums of distinct integral squares.

Nous déterminons tous les entiers totalement positifs qui ne peuvent pas être représentés comme des sommes de carrés distincts d'entiers dans Q(5).

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2008.05.008

Poo-Sung Park 1

1 School of Computational Sciences, Korea Institute for Advanced Study, Hoegiro 87, Dongdaemun-gu, Seoul, 130-722, Korea 
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Poo-Sung Park. Sums of distinct integral squares in $ \mathbb{Q}(\sqrt{5})$. Comptes Rendus. Mathématique, Volume 346 (2008) no. 13-14, pp. 723-725. doi : 10.1016/j.crma.2008.05.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.05.008/

[1] F. Götzky Über eine zahlentheoretische Anwendung von Modulfunktionen einer Veränderlichen, Math. Ann., Volume 100 (1928), pp. 411-437

[2] B.M. Kim On nonvanishing sum of integral squares of Q(5), Kangweon-Kyungki Math. J., Volume 6 (1998) no. 2, pp. 299-302

[3] H. Maass Über die Darstellung total positiver Zahlen des Körpers R(5) als Summe von drei Quadraten, Abh. Math. Sem. Hansischen Univ., Volume 14 (1941), pp. 185-191

[4] C.L. Siegel Sums of mth powers of algebraic integers, Ann. of Math., Volume 46 (1945), pp. 313-339 (Ges. Abh. III, pp. 12–46)

[5] R. Sprague Über Zerlegungen in ungleiche Quadratzahlen, Math. Z., Volume 51 (1949), pp. 289-290

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