SUMS OF (pr+ 1)-TH POWERS IN THE POLYNOMIAL RING Fpm[T]
Mireille Car · Journal of the Korean Mathematical Society · 2012
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 $M_i < k$ + degM.