Generalized Kummer theory and its applications
Annales mathématiques Blaise Pascal, Tome 16 (2009) no. 1, pp. 127-138.

In this report we study the arithmetic of Rikuna’s generic polynomial for the cyclic group of order n and obtain a generalized Kummer theory. It is useful under the condition that ζk and ωk where ζ is a primitive n-th root of unity and ω=ζ+ζ -1 . In particular, this result with ζk implies the classical Kummer theory. We also present a method for calculating not only the conductor but also the Artin symbols of the cyclic extension which is defined by the Rikuna polynomial.

DOI : 10.5802/ambp.259
Classification : 11R20, 12E10, 12G05
Mots clés : Generic polynomial, Kummer theory, Artin symbol
Toru Komatsu 1

1 Faculty of Mathematics Kyushu University 6-10-1 Hakozaki Higashiku Fukuoka, 812-8581 Japan
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Toru Komatsu. Generalized Kummer theory and its applications. Annales mathématiques Blaise Pascal, Tome 16 (2009) no. 1, pp. 127-138. doi : 10.5802/ambp.259. https://ambp.centre-mersenne.org/articles/10.5802/ambp.259/

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