1. Equidistribution in the dual group of the $S$-adic integers
- Creator:
- Urban, Roman
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- uniform distribution modulo $1$, equidistribution in probability, algebraic number fields, $S$-adele ring, $S$-integer dynamical system, algebraic dynamics, topological dynamics, and $a$-adic solenoid
- Language:
- English
- Description:
- Let $X$ be the quotient group of the $S$-adele ring of an algebraic number field by the discrete group of $S$-integers. Given a probability measure $\mu $ on $X^d$ and an endomorphism $T$ of $X^d$, we consider the relation between uniform distribution of the sequence $T^n\bold {x}$ for $\mu $-almost all $\bold {x}\in X^d$ and the behavior of $\mu $ relative to the translations by some rational subgroups of $X^d$. The main result of this note is an extension of the corresponding result for the $d$-dimensional torus $\mathbb T^d$ due to B. Host.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public