Normality of some p—adic product expansions

Abstract

AbstractWe consider two unique products for a given p—adic integer x with leading coefficient 1, where anbn ∈ {0, 1,… p − 1}. It is shown that, for almost all such x relative to Haar measure on the p—adic integers, the sequences (an), (bn) are normal to base p, and have standard normal distribution functions.