Submission: 2012, Nov 15, revised 2012, Nov 21
We show that the pythagoras number of a real function field is strictly larger than its transcendence degree. In the purely transcendental case, this is a well known consequence of the Cassels-Pfister theorem.
2010 Mathematics Subject Classification: 12D15, 13J30, 14C17
Keywords and Phrases: pythagoras number, real function fields, valuations on function fields
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