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Subjects
11-XX Number theory
11Rxx Algebraic number theory: global fields
11R20 Other abelian and metabelian extensions

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Galois generators and the subspace theorem.

G.R. Everest (1986/1987)

Manuscripta mathematica

Gaussian primes

Etienne Fouvry, Henryk Iwaniec (1997)

Acta Arithmetica

Generalized Kummer theory and its applications

Toru Komatsu (2009)

Annales mathématiques Blaise Pascal

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 $ζ \notin k$ and $ω \in k$ where $ζ$ is a primitive $n$ -th root of unity and $ω = ζ + ζ^{- 1}$ . In particular, this result with $ζ \in k$ 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.

Good reduction of elliptic curves in abelian extensions.

Ian Connell (1993)

Journal für die reine und angewandte Mathematik

Currently displaying 1 – 4 of 4

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