This research demonstrates that every sum of squares in transcendence degree 1 fields equals 5 squares, suggesting new pathways in quadratic form representation.
We show that any sum of squares in a field of transcendence degree $1$ over Q is a sum of $5$ squares, answering a question of Pop and Pfister. We deduce this result from a representation theorem, in $k(C)$, for quadratic forms of rank ≥ 5 with coefficients in k, where C is a curve over a number field k.
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Olivier Benoist (2025) studied this question.
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