Semi-local units modulo Gauss sums |
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| Authors: | Yoshitaka Hachimori Humio Ichimura |
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| Institution: | Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1, Komaba, Meguro-ku, Tokyo, 153, Japan.?e-mail: yhachi@ms.u-tokyo.ac.jp}, JP
Department of Mathematics, Yokohama City University, 22-2, Seto, Kanazawa-ku, Yokohama, 236, Japan, JP
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| Abstract: | 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”.
Received: 2 May 1997 / Revised version: 11 November 1997 |
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