Generalized Kummer theory and its applications
نویسنده
چکیده
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 ζ 6∈ k and ω ∈ k where ζ is a primitive n-th root of unity and ω = ζ + ζ−1. In particular, this result with ζ ∈ k 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.
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