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The calculation of a large cubic class number with an application to real cyclotomic fields. (English) Zbl 0527.12004

The class number of the cubic subfield of the \(p\)th cyclotomic field is calculated for the prime \(p = 11290018777\). This is used to construct an example where the class number of the \(p\)th real cyclotomic field is larger than \(p\).
Reviewer: H. C. Williams

MSC:

11Y40 Algebraic number theory computations
11R18 Cyclotomic extensions
11R29 Class numbers, class groups, discriminants
11R16 Cubic and quartic extensions
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