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- W4299600477 abstract "In 1888, Hilbert proved that every non-negative 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. Up to now, no elementary proof is known. Here we present a completely new approach. Although our proof is not easy, it uses only elementary techniques. As a by-product, it gives information on the number of representations f=p_1^2+p_2^2+p_3^2 of f up to orthogonal equivalence. We show that this number is 8 for generically chosen f, and that it is 4 when f is chosen generically with a real zero. Although these facts were known, there was no elementary approach to them so far." @default.
- W4299600477 created "2022-10-02" @default.
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- W4299600477 date "2010-09-16" @default.
- W4299600477 modified "2023-09-27" @default.
- W4299600477 title "An elementary proof of Hilbert's theorem on ternary quartics" @default.
- W4299600477 doi "https://doi.org/10.48550/arxiv.1009.3144" @default.
- W4299600477 hasPublicationYear "2010" @default.
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