On periodic \(p\)-adic distributions (Q2440381)

Let \(p\) be a prime number and let \(\mathbb{Z}_p\) denote the ring of \(p\)-adic integers. The author introduces the notion of a periodic \(p\)-adic distribution on \(\mathbb{Z}_p\), with the periodicity of the distribution depending on the partition of \(\mathbb{Z}_p\). Then the author presents several partitions of \(\mathbb{Z}_p\) for each of which he gives a characterization of all the corresponding periodic \(p\)-adic distributions on \(\mathbb{Z}_p\). If the distribution is bounded, then it is called a measure; the author gives an example of such a periodic \(p\)-adic measure on \(\mathbb{Z}_p\).