Improved bounds on Gauss sums in arbitrary finite fields

Abstract

Let [Formula: see text] be a power of a prime and let [Formula: see text] be the finite field consisting of [Formula: see text] elements. We establish new explicit estimates on Gauss sums of the form [Formula: see text], where [Formula: see text] is a nontrivial additive character. In particular, we show that one has a nontrivial upper bound on [Formula: see text] for certain values of [Formula: see text] of order up to [Formula: see text]. Our results improve on the previous best-known bound due to Zhelezov.

Locations

• International Journal of Number Theory - View
• arXiv (Cornell University) - View - PDF
• DataCite API - View