I'm trying to read this paper: http://www.springerlink.com/content/g0046660260825x3/

or http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.20.1813&rep=rep1&type=pdf

But I don't understand the norm they are using in (1.3). Context suggests to me that it should be a related to how easy it is to approximate an irrational number with rationals, but they don't have a definition in the paper, and I don't think I understand Diophantine approximation well enough to guess what it is.