Sums of squares in rings of integers with 2 inverted
Gaël Collinet
Acta Arithmetica, Tome 172 (2016), p. 383-390 / Harvested from The Polish Digital Mathematics Library
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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.

Publié le : 2016-01-01
EUDML-ID : urn:eudml:doc:286411 
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     author = {Ga\"el Collinet},
     title = {Sums of squares in rings of integers with 2 inverted},
     journal = {Acta Arithmetica},
     volume = {172},
     year = {2016},
     pages = {383-390},
     zbl = {06602746},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa8363-2-2016}
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Gaël Collinet. Sums of squares in rings of integers with 2 inverted. Acta Arithmetica, Tome 172 (2016) pp. 383-390. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa8363-2-2016/