By an elementary approach, we derive the value of the Gauss sum of a cubic character over a finite field without using Davenport-Hasse’s theorem (namely, if s is odd the Gauss sum is -1, and if s is even its value is ).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba59-1-2,
author = {Davide Schipani and Michele Elia},
title = {Gauss Sums of the Cubic Character over $GF(2^m)$: an Elementary Derivation},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {59},
year = {2011},
pages = {11-18},
zbl = {1215.11117},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba59-1-2}
}
Davide Schipani; Michele Elia. Gauss Sums of the Cubic Character over $GF(2^m)$: an Elementary Derivation. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 59 (2011) pp. 11-18. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba59-1-2/