Gauss sums of the cubic character over \(\text{GF}(2^m)\): an elementary derivation. (English) Zbl 1215.11117

Schipani, Davide; Elia, Michele

Bull. Pol. Acad. Sci., Math. 59, No. 1, 11-18 (2011).

Summary: By an elementary approach, we derive the value of the Gauss sum of a cubic character over a finite field \({\mathbb F}_{2^s} \) without using Davenport-Hasse’s theorem (namely, if \(s\) is odd, the Gauss sum is \(-1\), and if \(s\) is even its value is \((-2)^\frac{s}{2}\)).

MSC:

11T24

Other character sums and Gauss sums

Keywords:

Gauss sum;cubic character; finite fields of characteristic \(2\)