JournalspmVol. 67 / No. 1DOI 10.4171/pm/1856

Sums of (2<sup><var>r<var></sup>&#8201;+&#8201;1)-th powers in the polynomial ring <b>F</b><sub>2<sup><var>m</var></sup></sub>[<var>T</var>]

  • Mireille Car

    Université Aix-Marseille III, France
Sums of (2<sup><var>r<var></sup>&#8201;+&#8201;1)-th powers in the polynomial ring <b>F</b><sub>2<sup><var>m</var></sup></sub>[<var>T</var>] cover

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supp { vertical-align: 0.8ex; font-size:75%; } subb { vertical-align: -0.8ex; font-size:75%; } .ions { line-height: 1.8; } .ions subb {position: relative; top: 4; left: 1; } .ions supp {position: absolute; top: 70; left:985; } Let F be a finite field with 2m elements and let k = 2r + 1. We study representations and strict representations of polynomials M ∈ F[T] by sums of k-th powers. A representation

M = Mk1 + ··· + Mks

of M ∈ F[T] as a sum of k-th powers of polynomials is strict if k deg Mi < k + deg M.