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

详细

This article introduces several rotation and additive invariant ultrametrics on the finite adèle ring A_f of the rational numbers ℚ. 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 A_f.