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Cyclic Polynomials Arising from Kummer Theory of Norm Algebraic Tori

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Algorithmic Number Theory (ANTS 2006)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 4076))

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Abstract

We study cyclic extensions arising from Kummer theory of norm algebraic tori. In particular, we compute quintic cyclic polynomials defining ‘Kummer extension’. The polynomials do not only give all the quintic cyclic extensions over the rationals by choosing the parameters but also classify all such extensions. Some arithmetic properties of the polynomials are also derived.

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Author information

Authors and Affiliations

  1. University of Electro-Communications, Chofu Tokyo, Japan

    Masanari Kida

Authors
  1. Masanari Kida
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Editor information

Editors and Affiliations

  1. Technische Universität Berlin, Germany

    Florian Hess

  2. Institut für Mathematik, MA 8–1, Technische Universität Berlin, Straße des 17. Juni 136, 10623, Berlin, Germany

    Sebastian Pauli

  3. Institut für Mathematik, Technische Universität Berlin, Fakultät II, MA 8-1, Strasse des 17. Juni 136, 10623, Berlin, Germany

    Michael Pohst

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© 2006 Springer-Verlag Berlin Heidelberg

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Kida, M. (2006). Cyclic Polynomials Arising from Kummer Theory of Norm Algebraic Tori. In: Hess, F., Pauli, S., Pohst, M. (eds) Algorithmic Number Theory. ANTS 2006. Lecture Notes in Computer Science, vol 4076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11792086_8

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  • DOI: https://doi.org/10.1007/11792086_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-36075-9

  • Online ISBN: 978-3-540-36076-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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