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Gauss Sums of Cubic Characters over $\mathbb F_{p^r}$, $p$ Odd

Volume 60 / 2012

Davide Schipani, Michele Elia Bulletin Polish Acad. Sci. Math. 60 (2012), 1-19 MSC: Primary 11T24; Secondary 11T06. DOI: 10.4064/ba60-1-1

Abstract

An elementary approach is shown which derives the values of the Gauss sums over $\mathbb F_{p^r}$, $p$ odd, of a cubic character. New links between Gauss sums over different field extensions are shown in terms of factorizations of the Gauss sums themselves, which are then revisited in terms of prime ideal decompositions. Interestingly, one of these results gives a representation of primes $p$ of the form $6k+1$ by a binary quadratic form in integers of a subfield of the cyclotomic field of the $p$th roots of unity.

Authors

  • Davide SchipaniInstitute of Mathematics
    University of Zürich
    Zürich, Switzerland
    e-mail
  • Michele EliaDepartment of Electronics
    Politecnico di Torino
    10129 Torino, Italy
    e-mail

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