Gauss Sums of the Cubic Character over ${\rm GF}(2^m)$: an Elementary Derivation

Volume 59 / 2011

Davide Schipani, Michele Elia Bulletin Polish Acad. Sci. Math. 59 (2011), 11-18 MSC: Primary 12Y05; Secondary 12E30. DOI: 10.4064/ba59-1-2


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 $-(-2)^{s/2}$).


  • Davide SchipaniInstitute of Mathematics
    University of Zurich
    8057 Zürich, Switzerland
  • Michele EliaDepartment of Electronics
    Politecnico di Torino
    10129 Torino, Italy

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