Sums of seventh powers in the polynomial ring $\mathbb{F}_{2^{m}}[T]$

Mireille Car

doi:10.4171/pm/1893

JournalspmVol. 68, No. 3pp. 297–316

Sums of seventh powers in the polynomial ring $\mathbb{F}_{2^{m}}[T]$

Mireille Car
Université Aix-Marseille III, France

$Sums of seventh powers in the polynomial ring $\mathbb{F}_{2^{m}}[T]$ cover$

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Abstract

Let $F$ be a finite field with even characteristic and $q\geq16$ elements. We study representations of polynomials $P\in F[T]$ as sums $P = X_{1}^{7} +\cdots + X_{s}^{7}$ .

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Mireille Car, Sums of seventh powers in the polynomial ring $\mathbb{F}_{2^{m}}[T]$ . Port. Math. 68 (2011), no. 3, pp. 297–316

DOI 10.4171/PM/1893