Geodesic
Sums of squares in rings of integers with 2 inverted
Gaël Collinet1
1 IRMA, Université de Strasbourg et CNRS 7 rue René Descartes 67084 Strasbourg, France
Acta Arithmetica, Tome 173 (2016) no. 4, pp. 383-390.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We prove that in a ring of $S$-integers containing ${1}/{2}$, any totally positive element is a sum of five squares. We also exhibit examples of such rings where some totally positive elements cannot be written as the sum of four squares.
DOI : 10.4064/aa8363-2-2016
Keywords: prove ring s integers containing totally positive element sum five squares exhibit examples rings where totally positive elements cannot written sum squares

Gaël Collinet 1

1 IRMA, Université de Strasbourg et CNRS 7 rue René Descartes 67084 Strasbourg, France 
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Gaël Collinet. Sums of squares in rings of integers with 2 inverted. Acta Arithmetica, Tome 173 (2016) no. 4, pp. 383-390. doi : 10.4064/aa8363-2-2016. http://geodesic.mathdoc.fr/articles/10.4064/aa8363-2-2016/

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