Waring's problem for polynomial biquadrates over a finite field of odd characteristic

Car, Mireille; Gallardo, Luis H.

Funct. Approx. Comment. Math., Tome 37 (2007) no. 1, p. 39-50 / Harvested from Project Euclid

Résumé

Let $q$ be a power of an odd prime $p$ and let ${k}$ be a finite field with $q$ elements. Our main result is: If $q \notin \{3,9,5,13,17,25,29\},$ every polynomial $P\in{k}[t]$ of degree $\geq 269$ is a strict sum of 11 biquadrates. We first decompose $P$ as a strict mixed sum of biquadrates.

Publié le : 2007-01-15
Classification: Waring's problem, biquadrates, polynomials, finite fields, odd characteristic, 11T55, 11P05, 11D85

@article{1229618740,
     author = {Car, Mireille and Gallardo, Luis H.},
     title = {Waring's problem for polynomial biquadrates over a finite field of odd characteristic},
     journal = {Funct. Approx. Comment. Math.},
     volume = {37},
     number = {1},
     year = {2007},
     pages = { 39-50},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1229618740}
}

Car, Mireille; Gallardo, Luis H. Waring's problem for polynomial biquadrates over a finite field of odd characteristic. Funct. Approx. Comment. Math., Tome 37 (2007) no. 1, pp.  39-50. http://gdmltest.u-ga.fr/item/1229618740/