Class groups, totally positive units, and squares
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- by H. M. Edgar, R. A. Mollin and B. L. Peterson PDF
- Proc. Amer. Math. Soc. 98 (1986), 33-37 Request permission
Abstract:
Given a totally real algebraic number field $K$, we investigate when totally positive units, $U_K^ +$, are squares, $U_K^2$. In particular, we prove that the rank of $U_K^ + /U_K^2$ is bounded above by the minimum of (1) the $2$-rank of the narrow class group of $K$ and (2) the rank of $U_L^ + /U_L^2$ as $L$ ranges over all (finite) totally real extension fields of $K$. Several applications are also provided.References
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Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 98 (1986), 33-37
- MSC: Primary 11R37; Secondary 11R27
- DOI: https://doi.org/10.1090/S0002-9939-1986-0848870-X
- MathSciNet review: 848870