HILBERT-SPEISER NUMBER FIELDS AND STICKELBERGER IDEALS; THE CASE p = 2

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Abstract

We say that a number field F satisfies the condition (H′<sub>2<sup>m</sup></sub>) when any abelian extension of exponent dividing 2<sup>m </sup> has a normal basis with respect to rings of 2-integers. We say that it satisfies (H′<sub>2<sup>∞</sup></sub>) when it satisfies (H′<sub>2<sup>m</sup></sub>) for all m. We give a condition for F to satisfy (H'<sub>2<sup>m</sup></sub>), and show that the imaginary quadratic fields F = Q(√−1) and Q(√−2) satisfy the very strong condition (H′<sub>2<sup>∞</sup></sub>) if the conjecture that h<sup>+</sup><sub>2<sup>m</sup></sub> = 1 for all m is valid. Here, h<sup>+</sup><sub>2<sup>m</sup></sub>) is the class number of the maximal real abelian field of conductor 2<sup>m</sup>.

Journal

  • Mathematical Journal of Okayama University

    Mathematical Journal of Okayama University 54(1), 33-48, 2012-01

    Department of Mathematics, Faculty of Science, Okayama University

Codes

  • NII Article ID (NAID)
    120003610062
  • NII NACSIS-CAT ID (NCID)
    AA00723502
  • Text Lang
    ENG
  • Article Type
    journal article
  • ISSN
    0030-1566
  • Data Source
    IR 
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