Geodesic
SUMS OF CUBES AND SQUARES OF POLYNOMIALS WITH COEFFICIENTS IN A FINITE FIELD
Glasgow mathematical journal, Tome 51 (2009) no. 1, pp. 161-186

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.1017/S0017089508004618
Mots-clés : 11T55, 11R58 
CAR, MIREILLE; GALLARDO, LUIS H. SUMS OF CUBES AND SQUARES OF POLYNOMIALS WITH COEFFICIENTS IN A FINITE FIELD. Glasgow mathematical journal, Tome 51 (2009) no. 1, pp. 161-186. doi: 10.1017/S0017089508004618
@article{10_1017_S0017089508004618,
     author = {CAR, MIREILLE and GALLARDO, LUIS H.},
     title = {SUMS {OF} {CUBES} {AND} {SQUARES} {OF} {POLYNOMIALS} {WITH} {COEFFICIENTS} {IN} {A} {FINITE} {FIELD}},
     journal = {Glasgow mathematical journal},
     pages = {161--186},
     year = {2009},
     volume = {51},
     number = {1},
     doi = {10.1017/S0017089508004618},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089508004618/}
}
TY  - JOUR
AU  - CAR, MIREILLE
AU  - GALLARDO, LUIS H.
TI  - SUMS OF CUBES AND SQUARES OF POLYNOMIALS WITH COEFFICIENTS IN A FINITE FIELD
JO  - Glasgow mathematical journal
PY  - 2009
SP  - 161
EP  - 186
VL  - 51
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089508004618/
DO  - 10.1017/S0017089508004618
ID  - 10_1017_S0017089508004618
ER  - 
%0 Journal Article
%A CAR, MIREILLE
%A GALLARDO, LUIS H.
%T SUMS OF CUBES AND SQUARES OF POLYNOMIALS WITH COEFFICIENTS IN A FINITE FIELD
%J Glasgow mathematical journal
%D 2009
%P 161-186
%V 51
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089508004618/
%R 10.1017/S0017089508004618
%F 10_1017_S0017089508004618

[1] 1.Car, M. and Gallardo, L., Sums of cubes of polynomials, Acta Arith. 112 (1) (2004), 41–50. Google Scholar | DOI

[2] 2.Cassels, J. W. S., On the representation of rational functions as sums of squares, Acta Arith. 9 (1964), 79–82. Google Scholar | DOI

[3] 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. Google Scholar | DOI

[4] 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] 5.Linnik, Y. V., Additive problems involving squares, cubes and almost primes, Acta Arith. 21 (1972), 413–422. Google Scholar | DOI

[6] 6.Pfister, A., Multiplikative Quadratische Formen, Arch. Math. 16 (1965), 363–370. Google Scholar | DOI

[7] 7.Serre, J.-P., Conférence au S/'eminaire de Th/'eorie des nombres de Bordeaux (Juin 1982). Google Scholar

[8] 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] 9.Vaserstein, L. N., Sums of cubes in polynomials rings, Math. Comp. 56 (1991), 349–357. Google Scholar | DOI

Cité par Sources :