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http://dx.doi.org/10.4134/JKMS.2012.49.6.1139

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

Car, Mireille (Amu, Case Cour A Avenue Escadrille Normandie-Niemen)
Publication Information
Journal of the Korean Mathematical Society / v.49, no.6, 2012 , pp. 1139-1161 More about this Journal
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 $M{\in}F$[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.
Keywords
finite fields; polynomials; Waring's problem;
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