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Congruences for the class numbers of real cyclic sextic number fields. (English) Zbl 0991.11057

Extending results on quadratic and cyclic quartic fields the author studies the class number \(h\) of real cyclic sextic number fields \(K\). Seven congruences are obtained. In particular when the conductor of \(K\) is a prime \(p\), then \[ C\cdot h^-\equiv B_{{p-1}\over{6}}\cdot B_{{5(p-1)}\over{6}} (\bmod p) \] where \(C\) is an explicitly given constant.
Reviewer: I.Gaál (Debrecen)

MSC:

11R29 Class numbers, class groups, discriminants
11R21 Other number fields
11B68 Bernoulli and Euler numbers and polynomials
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References:

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