Journal of the
Korean Mathematical Society JKMS

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 $M\in F[T]$ by sums of $(p^{r}+1)$-th powers. A representation $$M = M_{1}^{k}+\cdots+ M_{s}^{k}$$ of $M\in F[T]$ as a sum of $k$-th powers of polynomials is strict if $ k\deg M_{i} < k + \deg M$.

Keywords: finite fields, polynomials, Waring's problem

MSC numbers: Primary 11T55; Secondary 11R58