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SUMS OF CUBES AND SQUARES OF POLYNOMIALS WITH COEFFICIENTS IN A FINITE FIELD

Published online by Cambridge University Press:  01 January 2009

MIREILLE CAR  and
LUIS H. GALLARDO
MIREILLE CAR
Affiliation:
Université Paul Cézanne Aix-Marseille III, LATP, Faculté des Sciences et Techniques, Case cour A, Avenue Escadrille Normandie-Niemen, 13397 Marseille Cedex 20, France e-mail: [email protected]
LUIS H. GALLARDO
Affiliation:
Département de Mathématiques, Université de Brest, 6, Avenue Victor Le Gorgeu, C.S. 93837, 29238 Brest Cedex 3, France e-mail: [email protected]
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Abstract

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Let k be a finite field with q elements and characteristic coprime with 6. Our main result is: Every polynomial P ∈ k[T] is a strict sum of three cubes and two squares.

Keywords

11T5511R58
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 51 , Issue 1 , January 2009 , pp. 161 - 186
Copyright
Copyright © Glasgow Mathematical Journal Trust 2008

References

REFERENCES

1.Car, M. and Gallardo, L., Sums of cubes of polynomials, Acta Arith. 112 (1) (2004), 41–50.CrossRefGoogle Scholar
2.Cassels, J. W. S., On the representation of rational functions as sums of squares, Acta Arith. 9 (1964), 79–82.CrossRefGoogle Scholar
3.Effinger, G. and Hayes, D. R., Additive number theory of polynomials over a finite field Oxford Mathematical Monographs (Clarendon Press, Oxford, 1991), xvi, 157.CrossRefGoogle Scholar
4.Gallardo, L., Waring's problem for polynomial cubes and squares over a finite field with odd characteristic, Port. Math. (N. S.) 61 (1), (2004), 35–49.Google Scholar
5.Linnik, Y. V., Additive problems involving squares, cubes and almost primes, Acta Arith. 21 (1972), 413–422.CrossRefGoogle Scholar
6.Pfister, A., Multiplikative Quadratische Formen, Arch. Math. 16 (1965), 363–370.CrossRefGoogle Scholar
7.Serre, J.-P., Conférence au S/'eminaire de Th/'eorie des nombres de Bordeaux (Juin 1982).Google Scholar
8.Stepanov, S. A., Arithmetic of algebraic curves, (Translation. from Russian by Aleksanova, Irene), Monographs in Contemporary Mathematics, (New York, NY: Consultants Bureau, A divison of Plenum Publishing Co. xii, 422 p (1994).Google Scholar
9.Vaserstein, L. N., Sums of cubes in polynomials rings, Math. Comp. 56 (1991), 349–357.CrossRefGoogle Scholar