Q:

When are all signatures represented by units?

What conditions on a number field imply that every signature is represented by a unit? Are there conditions that imply that it is not the case that every signature is represented by a unit?
For example, if K is a cubic cyclic number field with odd class number then all signatures are represented by units by Theorem V in [Armitage, J., & Fröhlich, A. (1967). Classnumbers and unit signatures. Mathematika, 14(1), 94-98. doi:10.1112/S0025579300008044].
What are some references for articles on this topic?

A:

The structure of the group of units modulo totally positive units is studied here; see also the references in this article. Since then, relevant articles by Dummit and Dummit & Voight have appeared.

