Sums of squares in rings of integers with 2 inverted

Gaël Collinet. "Sums of squares in rings of integers with 2 inverted." Acta Arithmetica 173.4 (2016): 383-390. <http://eudml.org/doc/286411>.

@article{GaëlCollinet2016,
abstract = {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.},
author = {Gaël Collinet},
journal = {Acta Arithmetica},
keywords = {sums of squares; rings of (S)-integers; universal forms},
language = {eng},
number = {4},
pages = {383-390},
title = {Sums of squares in rings of integers with 2 inverted},
url = {http://eudml.org/doc/286411},
volume = {173},
year = {2016},
}

TY - JOUR
AU - Gaël Collinet
TI - Sums of squares in rings of integers with 2 inverted
JO - Acta Arithmetica
PY - 2016
VL - 173
IS - 4
SP - 383
EP - 390
AB - 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.
LA - eng
KW - sums of squares; rings of (S)-integers; universal forms
UR - http://eudml.org/doc/286411
ER -