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The relative class numbers of imaginary cyclic fields of degrees 4, 6, 8, and 10. (English) Zbl 0787.11046
For an imaginary abelian field $$K$$, let $$n$$ be the conductor and $$h^ -$$ the relative class number of $$K$$. Let $$K^ +$$ denote the maximal real subfield of $$K$$. The author derives a formula for $$h^ -$$ in terms of a generalized Maillet determinant, provided no prime factor of $$n$$ splits in $$K/K^ +$$. He then specializes to $$n = p$$, an odd prime, and writes down the determinant involved given that $$K$$ is of degree 4, 6, 8, or 10. In these cases he applies the formula to compute $$h^ -$$ for $$p < 500,000$$. A supplement displays the results for the degrees 6, 8, and 10 up to $$p < 10,000$$.

##### MSC:
 11R29 Class numbers, class groups, discriminants 11R20 Other abelian and metabelian extensions 11-04 Software, source code, etc. for problems pertaining to number theory
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