Bounds of Gauss Sums in Finite Fields

Abstract

We consider Gauss sums of the form Gn(a) = ∑ x∈Fpm χ(x) with a nontrivial additive character χ 6= χ0 of a finite field Fpm of pm elements of characteristic p. The classical bound |Gn(a)| ≤ (n−1)pm/2 becomes trivial for n ≥ pm/2 + 1. We show that, combining some recent bounds of HeathBrown and Konyagin with several bounds due to Deligne, Katz, and Li, one… (More)

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Cite this paper

@inproceedings{Shparlinski2004BoundsOG, title={Bounds of Gauss Sums in Finite Fields}, author={Igor E. Shparlinski and Wen-Ching Winnie Li}, year={2004} }