1. BINARY FORMS WITH THREE DIFFERENT RELATIVE RANKS.
- Author
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REZNICK, BRUCE and TOKCAN, NERIMAN
- Subjects
- *
SYLVESTER matrix equations , *DESCARTES'S rule of signs (Mathematics) , *HYPERBOLIC functions , *MATHEMATICS theorems - Abstract
Suppose f(x, y) is a binary form of degree d with coefficients in a field K ⊆ C. The K-rank of f is the smallest number of d-th powers of linear forms over K of which f is a K-linear combination. We prove that for d ≥ 5, there always exists a form of degree d with at least three different ranks over various fields. The K-rank of a form f (such as x3y2) may depend on whether -1 is a sum of two squares in K. [ABSTRACT FROM AUTHOR]
- Published
- 2017
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