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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



The relative class numbers of imaginary cyclic fields of degrees $ 4,\;6,\;8,$ and $ 10$

Author: Kurt Girstmair
Journal: Math. Comp. 61 (1993), 881-887, S25
MSC: Primary 11R29; Secondary 11R18, 11R20, 11Y40
MathSciNet review: 1195428
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Abstract: We express the relative class number of an imaginary abelian number field K of prime power conductor as a sort of Maillet determinant. Thereby we obtain explicit relative class number formulas for fields K of conductor p, $ p \geq 3$ prime, and degree $ 2d = [K:\mathbb{Q}] \leq 10$, in terms of sums of 2d-power residues. In particular, tables are given for $ p \leq 10000$.

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Article copyright: © Copyright 1993 American Mathematical Society

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