Polynomial Power Residue Symbols and $q$-resultants

C. R. Math. Rep. Acad. Sci. Canada Vol. 39 (2) 2017, pp. 60-66
(Received: 2016-03-17 , Revised: 2016-05-22)

Yoshinori Hamahata,Department of Applied Mathematics, Okayama University of Science, Ridai-cho 1-1, Okayama, 700{0005, Japan; e-mail: hamahata@xmath.ous.ac.jp

Abstract/Résumé:

We establish a relation between polynomial power residue symbols and \(q\)-resultants of \(\mathbb{F}_q\)-linear polynomials. We then establish the \(q-1\)-st power reciprocity law.

On établit une relation entre le symbole de résidu de puissances en caractéristique \(p\) et le \(q\)-résultant de deux \(\mathbb{F}_q\)-polynômes linéaire. Alors on démontre la loi de réciprocité des puissances \(q-1\)-èmes.

Keywords: Power residues, function fields., reciprocity law

AMS Subject Classification: Power residues; reciprocity, Drinfeld modules; higher-dimensional motives; etc., Arithmetic theory of polynomial rings over finite fields 11A15, 11G09, 11T55

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