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Séminaire de Théorie Analytique des Nombres et Problèmes
Diophantiens

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Le 12 avril 2001

Luis Gallardo (Brest)

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Sums of squares and k-th powers in **F*_{q}[*t*]

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**Abstract**:
Let *q* be such that -1 is a square in *Fq*.Every polynomial in *F*_{q}[*t*] that has sufficiently large degree
is a strict sum of O(k) k-th powers and 2 squares.
For *k*=3 the more precise result is true:
Every polynomial in *F*_{q}[*t*] is a strict sum of 3 cubes
and 2 squares. If -1 is not a square in Fq, every polynomial
in *F*_{q}[*t*] is a strict sum of 4 cubes
and 2 squares.
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