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On the Proximity of Algebraic Units To Divisors

✍ Scribed by G.R. Everest

Publisher: Elsevier Science
Year: 1995
Tongue: English
Weight: 493 KB
Volume: 50
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1995.1018

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✦ Synopsis

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. 1995 Academic Press. Inc

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