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Solution of the class number two problem for cyclotomic fields. (English) Zbl 0288.12005
It is shown that the only cyclotomic fields of the form \(\mathbb Q(e^{2\pi i/m})\) which have class number two are \(\mathbb Q(e^{2\pi i/39})\) and \(\mathbb Q(e^{2\pi i/56})\). Methods are the same as used in solving the class number one problem [the author and H. L. Montgomery, J. Reine Angew. Math. 286/287, 248–256 (1976; Zbl 0335.12013)].
Reviewer: John Myron Masley

MSC:
11R29 Class numbers, class groups, discriminants
11R18 Cyclotomic extensions
11R42 Zeta functions and \(L\)-functions of number fields
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References:
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