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arXiv · 2411.08479

An elementary proof of Hilbert's theorem on ternary quartics: Some complements

Albrecht Pfister·Claus Scheiderer
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Abstract

In 1888, Hilbert proved that every nonnegative quartic form $f=f(x,y,z)$ with real coefficients is a sum of three squares of quadratic forms. His proof was ahead of its time and used advanced methods from topology and algebraic geometry. In a 2012 paper we presented a new approach that used only elementary techniques. In this note we add some further simplifications to this proof.

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Albrecht Pfister, Claus Scheiderer. 2024-11-13. An elementary proof of Hilbert's theorem on ternary quartics: Some complements. https://arxiv.org/abs/2411.08479

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