manuscripta mathematica

, Volume 95, Issue 3, pp 377–395 | Cite as

Semi-local units modulo Gauss sums

  • Yoshitaka Hachimori
  • Humio Ichimura


For the p-th cyclotomic field k, Iwasawa proved that p does not divide the class number of its maximal real subfield if and only if the odd part of the group of local units coincides with its subgroup generated by Jacobi sums related to k. We refine and give a quantitative version of this result for more general imaginary abelian fields. Our result is an analogy of the famous result on “semi-local units modulo cyclotomic units”.


Class Number Local Unit Quantitative Version Famous Result Cyclotomic Field 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Yoshitaka Hachimori
    • 1
  • Humio Ichimura
    • 2
  1. 1.Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1, Komaba, Meguro-ku, Tokyo, 153, Japan.¶e-mail:}JP
  2. 2.Department of Mathematics, Yokohama City University, 22-2, Seto, Kanazawa-ku, Yokohama, 236, JapanJP

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