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Gauss Sums of the Cubic Character over ${\rm GF}(2^m)$: an Elementary Derivation
Davide Schipani 1   ; Michele Elia 2
1 Institute of Mathematics University of Zurich 8057 Zürich, Switzerland
2 Department of Electronics Politecnico di Torino 10129 Torino, Italy
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 59 (2011) no. 1, pp. 11-18 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $-(-2)^{s/2}$).
DOI : 10.4064/ba59-1-2
Keywords: elementary approach derive value gauss sum cubic character finite field mathbb without using davenport hasses theorem namely odd gauss sum even its value

Davide Schipani  1   ; Michele Elia  2

1 Institute of Mathematics University of Zurich 8057 Zürich, Switzerland
2 Department of Electronics Politecnico di Torino 10129 Torino, Italy 
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Davide Schipani; Michele Elia. Gauss Sums of the Cubic Character over ${\rm GF}(2^m)$: an Elementary Derivation. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 59 (2011) no. 1, pp. 11-18. doi: 10.4064/ba59-1-2

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