Power Series with Coefficients from a Finite Set

TL;DR

This paper proves that multivariate D-finite power series with coefficients from a finite set are necessarily rational, extending previous rationality theorems to a broader class of series.

Contribution

It generalizes a 1996 rationality theorem to multivariate D-finite power series with finite set coefficients.

Findings

Multivariate D-finite power series with finite set coefficients are rational.

The result extends previous univariate cases to multivariate series.

Provides a broader understanding of the structure of D-finite series.

Abstract

We prove in this paper that a multivariate D-finite power series with coefficients from a finite set is rational. This generalizes a rationality theorem of van der Poorten and Shparlinski in 1996.