# Generalized Kummer theory and its applications

Toru Komatsu^{[1]}

- [1] Faculty of Mathematics Kyushu University 6-10-1 Hakozaki Higashiku Fukuoka, 812-8581 Japan

Annales mathématiques Blaise Pascal (2009)

- Volume: 16, Issue: 1, page 127-138
- ISSN: 1259-1734

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topKomatsu, Toru. "Generalized Kummer theory and its applications." Annales mathématiques Blaise Pascal 16.1 (2009): 127-138. <http://eudml.org/doc/10565>.

@article{Komatsu2009,

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

affiliation = {Faculty of Mathematics Kyushu University 6-10-1 Hakozaki Higashiku Fukuoka, 812-8581 Japan},

author = {Komatsu, Toru},

journal = {Annales mathématiques Blaise Pascal},

keywords = {Generic polynomial; Kummer theory; Artin symbol},

language = {eng},

month = {1},

number = {1},

pages = {127-138},

publisher = {Annales mathématiques Blaise Pascal},

title = {Generalized Kummer theory and its applications},

url = {http://eudml.org/doc/10565},

volume = {16},

year = {2009},

}

TY - JOUR

AU - Komatsu, Toru

TI - Generalized Kummer theory and its applications

JO - Annales mathématiques Blaise Pascal

DA - 2009/1//

PB - Annales mathématiques Blaise Pascal

VL - 16

IS - 1

SP - 127

EP - 138

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

LA - eng

KW - Generic polynomial; Kummer theory; Artin symbol

UR - http://eudml.org/doc/10565

ER -

## References

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