Arithmetic and metric properties of p-adic Engel series expansions

Abstract

We derive a characterization of rational numbers in terms of their unique p-adic Engel series expansions. Thereafter we investigate metric properties for the rational digits occurring in these p-adic Engel expansions. In particular, we obtain limiting distributions for the p-adic order of the digits and the p-adic order of approximation by the partial sums of the series expansions.