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”.
KeywordsClass Number Local Unit Quantitative Version Famous Result Cyclotomic Field
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