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Sums of squares in rings of integers with 2 inverted

Volume 173 / 2016

Gaël Collinet 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.

Authors

  • Gaël CollinetIRMA, Université de Strasbourg et CNRS
    7 rue René Descartes
    67084 Strasbourg, France
    e-mail

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