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- W2793491948 abstract "We give an algebraic proof of a class number formula for dihedral extensions of number fields of degree $2q$, where $q$ is any odd integer. Our formula expresses the ratio of class numbers as a ratio of orders of cohomology groups of units and recovers similar formulas which have appeared in the literature as special cases. As a corollary of our main result we obtain explicit bounds on the (finitely many) possible values which can occur as ratio of class numbers in dihedral extensions. Such bounds are obtained by arithmetic means, without resorting to deep integral representation theory." @default.
- W2793491948 created "2018-03-29" @default.
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- W2793491948 date "2019-05-21" @default.
- W2793491948 modified "2023-09-23" @default.
- W2793491948 title "CLASS NUMBER FORMULA FOR DIHEDRAL EXTENSIONS" @default.
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- W2793491948 doi "https://doi.org/10.1017/s0017089519000144" @default.
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