Bounds of Gauss sums in finite fields

Igor E. Shparlinski*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

We consider Gauss sums of the form (Chemical Equation Presented) with a nontrivial additive character χ ≠ 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 Heath-Brown and Konyagin with several bounds due to Deligne, Katz, and Li, one can obtain the bound on |Gn(a)| which is nontrivial for the values of n of order up to pm/2+1/6. We also show that for almost all primes one can obtain a bound which is nontrivial for the values of n of order up to p m/2+1/2.

Original languageEnglish
Pages (from-to)2817-2824
Number of pages8
JournalProceedings of the American Mathematical Society
Volume132
Issue number10
DOIs
Publication statusPublished - Oct 2004

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