EVERY POLYNOMIAL OVER A FIELD CONTAINING 𝔽_{16} IS A STRICT SUM OF FOUR CUBES AND ONE EXPRESSION A^{2} + A

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 46, Issue 5, 2009, pp.941-947
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2009.46.5.941

Title & Authors

EVERY POLYNOMIAL OVER A FIELD CONTAINING 𝔽_{16} IS A STRICT SUM OF FOUR CUBES AND ONE EXPRESSION A^{2} + A

Gallardo, Luis H.;

Gallardo, Luis H.;

Abstract

Let q be a power of 16. Every polynomial [t] is a strict sum . The values of A,B,C,D,E are effectively obtained from the coefficients of P. The proof uses the new result that every polynomial [t], satisfying the necessary condition that the constant term Q(0) has zero trace, has a strict and effective representation as: . This improves for such q's and such Q's a result of Gallardo, Rahavandrainy, and Vaserstein that requires three polynomials F,G,H for the strict representation +F+GH. Observe that the latter representation may be considered as an analogue in characteristic 2 of the strict representation of a polynomial Q by three squares in odd characteristic.

Keywords

Waring's problem;quadratic polynomials;cubes;finite fields;characteristic 2;

Language

English

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