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- W2004691303 abstract "Let V be a finite additive subgroup of a field K of characteristic p >0. We consider sums of the form S h ( V :α)=∑ v ∈ V ( v +α) h for h ≥0 and α∈ K . In particular, we give necessary and sufficient conditions for the vanishing of S h ( V ; α), in terms of the digit sum in the base- p expansion of h , in the case that V has index p in K . The proof involves the polynomial f V ( x )=∏ v ∈ V ( x − v ). We define V † = f V ( K ). In the case that K is finite, the polynomial f V † can be viewed as a generalised trace Tr V : K → V which coincides with the usual trace if V is a subfield of K ." @default.
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- W2004691303 date "1999-07-01" @default.
- W2004691303 modified "2023-10-16" @default.
- W2004691303 title "Power Sums over Finite Subspaces of a Field" @default.
- W2004691303 doi "https://doi.org/10.1006/ffta.1999.0243" @default.
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