Abstract :
An asymptotic formula counting algebraic units with respect to a proximity function on the group variety is given. The proximity function measures the local distance to a divisor on the variety. The formula allows a natural definition of mean distance between the group and the divisor. By allowing the divisor to vary a description of the way global units are decorated around local geometric configurations follows. Inevitably, Leopoldt′s conjecture is encountered. Some special cases of the mean value are calculated illustrating a dependence upon the p-adic regulator. The main techniques in this research are Baker′s theorem, in its archimedean and p- adic versions, and the theory of uniform distribution of sequences.
