On arithmetic properties of coefficients of rational functions

David Geoffrey Cantor

Vol. 15 (1965), No. 1, 55–58

DOI: 10.2140/pjm.1965.15.55

Abstract

The purpose of this note is to prove the following generalization of a result of Polya:

Theorem. Let $\left\{a_n\right\}$ be a sequence of algebraic integers, and $f$ a nonzero polynomial with complex coefficients. If ${\sum }_{n=0}^{\infty }f\left(n\right)a_n{z}^n$ is a rational function, then so is ${\sum }_{n=0}^{\infty }{a}_n{z}^n$.

Mathematical Subject Classification

Primary: 12.30

Secondary: 10.76

Milestones

Received: 13 August 1963

Published: 1 March 1965