Sums of squares in rings of integers with 2 inverted
Volume 173 / 2016
Acta Arithmetica 173 (2016), 383-390
MSC: Primary 11E25; Secondary 11P05.
DOI: 10.4064/aa8363-2-2016
Published online: 18 May 2016
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.
