Invariant ultrametrics and Markov processes on the finite adèle ring of ?

摘要

This article introduces several rotation and additive invariant ultrametrics on the finite adèle ring Af of the rational numbers ?. Symmetry, regularity and uniqueness properties of these ultrametrics are provided. With these non-Archimedean metrics at hand it is possible to define a wide class of rotation and additive invariant Markov processes on Af.