On the rational function field of real curves without real points

Manuel Ojanguren

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.

Keywords


Real curves, quasi algebracally closed field

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DOI: http://dx.doi.org/10.1478/AAPP.972A1

Copyright (c) 2019 Manuel Ojanguren

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