Suppose K is a totally real number field and that O_K^*
is the group of units of the integers of K. In this talk I will
show how if one assumes Schanuel's conjecture about
logarithms of algebraic numbers, one can determine the zeta
function of K from the isometry class of the rational
vector space spanned by the image of the units of K under
the usual log map into a Euclidean space. This is joint
work with C. Rajan.