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On divisibility of the class number of real octic fields of a prime conductor \(p=n^ 4+16\) by \(p\). (English) Zbl 0818.11042
Let \(K\) be a real octic subfield of the \(p\)-th cyclotomic field, where \(p\) is a prime of the form \(n^ 4+16\). The author proves that \(p\) divides the class number of \(K\) if and only if \(p\) divides the numerator of at least one of the Bernoulli numbers \(B_{j(p- 1)/8}\) for \(j=1,3,5,7\). In a previous work [Abh. Math. Semin. Univ. Hamb. 64, 105- 124 (1994)] he used a similar method to obtain an analogous result for quintic fields.
11R29 Class numbers, class groups, discriminants
11R18 Cyclotomic extensions
11B68 Bernoulli and Euler numbers and polynomials
11R20 Other abelian and metabelian extensions
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