Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali (Jul 2019)
On the rational function field of real curves without real points
Abstract
Let F be the field of rational functions of a real algebraic curve without real points. It is well-known that in F we can express -1 as a sum of two squares. We show that -1 is also a sum of four fourth powers, six sixth powers, and so on.
