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Gauss sums of cubic characters over $\mathbb{F}_{p^{r}}$, $\mathit{p}$ odd


Schipani, Davide; Elia, Michele (2012). Gauss sums of cubic characters over $\mathbb{F}_{p^{r}}$, $\mathit{p}$ odd. Bulletin of the Polish Academy of Sciences, Mathematics, 60(1):1-19.

Abstract

An elementary approach is shown which derives the values of the Gauss sums over $\mathbb{F}_{p^{r}}$, $\mathit{p}$ 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 $\mathit{p}$ of the form 6$\mathit{k}$+1 by a binary quadratic form in integers of a subfield of the cyclotomic field of the $\mathit{p}th roots of unity.

Abstract

An elementary approach is shown which derives the values of the Gauss sums over $\mathbb{F}_{p^{r}}$, $\mathit{p}$ 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 $\mathit{p}$ of the form 6$\mathit{k}$+1 by a binary quadratic form in integers of a subfield of the cyclotomic field of the $\mathit{p}th roots of unity.

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Additional indexing

Item Type:Journal Article, not refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2012
Deposited On:07 Dec 2016 08:30
Last Modified:17 Feb 2018 01:55
Publisher:Instytut Matematyczny PAN, Warszawa, PL
ISSN:0239-7269
OA Status:Closed
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.4064/ba60-1-1

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