Gauss Sums of the Cubic Character over $GF(2^m)$: an elementary derivation

Details Gauss Sums of the Cubic Character over $GF(2^m)$: an elementary derivation Gauss Sums of the Cubic Character over $GF(2^m)$: an elementary derivation

2010-12-23

arxiv.org/abs/1012.5320v3

Mathematics

Number Theory

minor changes; accepted for publication in Bulletin of the Polish Academy of Sciences, Ser. Mathematics

Scientific paper

An elementary approach is shown which derives 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 $-(-2)^{s/2}$).

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