Séminaire de Théorie Analytique des Nombres et Problèmes
Diophantiens
Le 12 avril 2001
Luis Gallardo (Brest)
Sums of squares and k-th powers in Fq[t]
Abstract:
Let q be such that -1 is a square in Fq.Every polynomial in Fq[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 Fq[t] is a strict sum of 3 cubes
and 2 squares. If -1 is not a square in Fq, every polynomial
in Fq[t] is a strict sum of 4 cubes
and 2 squares.
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stan@math.u-bordeaux.fr