Class groups, totally positive units, and squares

Edgar, H. M.; Mollin, R. A.; Peterson, B. L.

doi:10.1090/S0002-9939-1986-0848870-X

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.

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