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International audienceLet 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

SUMS OF (pr+ 1)-TH POWERS IN THE POLYNOMIAL RING Fpm[T]

SUMS OF (p^r+ 1)-TH POWERS IN THE POLYNOMIAL RING F_p_m[T]