Sums of $(p^r+1)$-th powers in the polynomial ring $\Bbb F_{p^m}[T]$

Abstract : Let p be an odd prime number and let F be a finite field with p(m) elements. We study representations and strict representations of polynomials M epsilon F[T] by sums of (p(r) + 1)-th powers. A representation M = M-1(k) + ... + M-s(k) of M epsilon F[T] as a sum of k-th powers of polynomials is strict if k deg M-i < k + deg M.
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Mireille Car. Sums of $(p^r+1)$-th powers in the polynomial ring $\Bbb F_{p^m}[T]$. Journal of the Korean Mathematical Society, The Korean Mathematical Society, 2012, 49 (6), pp.1139-1161. ⟨10.4134/JKMS.2012.49.6.1139⟩. ⟨hal-01311343⟩

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