Gauss sums of cubic characters over $GF(p^r)$, $p$ odd

Details Gauss sums of cubic characters over $GF(p^r)$, $p$ odd Gauss sums of cubic characters over $GF(p^r)$, $p$ odd

2011-01-15

arxiv.org/abs/1101.3029v3

Mathematics

Number Theory

accepted for publication in Bulletin of the Polish Academy of Sciences Mathematics

Scientific paper

An elementary approach is shown which derives the values of the Gauss sums over $\mathbb F_{p^r}$, $p$ odd, of a cubic character without using Davenport-Hasse's theorem. New links between Gauss sums over different field extensions are shown in terms of factorizations of the Gauss sums themselves, which are then rivisited 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.

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