11A15 — 2 articles found.

Polynomial Power Residue Symbols and $q$-resultants

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

PDF(click to download): Polynomial Power Residue Symbols and $q$-resultants

Proof of a conjecture of Terjanian for regular primes

C. R. Math. Rep. Acad. Sci. Canada Vol. 18 (5) 1996, pp. 193–198
Vol.18 (5) 1996
C. Helou Details
(Received: 1996-07-31 )
(Received: 1996-07-31 )

C. Helou

Abstract/Résumé:

No abstract available but the full text pdf may be downloaded at the title link below.

Keywords:

AMS Subject Classification: Power residues; reciprocity, Higher degree equations; Fermat's equation, Cyclotomic extensions 11A15, 11D41, 11R18

PDF(click to download): Proof of a conjecture of Terjanian for regular primes