Gauss Sums of the Cubic Character over GF(2~m): an Elementary Derivation

摘要

Summary. By an elementary approach, we derive the value of the Gauss sum of a cubic character over a finite field F_2s 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)~(s/2)).