On arithmetic properties of the Taylor series of rational functions. II

David Geoffrey Cantor

Vol. 41 (1972), No. 2, 329–334

DOI: 10.2140/pjm.1972.41.329

Abstract

Suppose a_n,b_n, and c_n = a_nb_n are sequences of algebraic integers and that all b_n are nonzero. It is easy to verify that if both a(z) = ∑ _n=0^∞a_nzⁿ and b(z) = ∑ _n=0^∞b_nzⁿ are rational functions, then so is c(z) = ∑ _n=0^∞c_nzⁿ. We are interested in studying the conjecture that if b(z) and c(z) are rational functions, then so is a(z). We shall prove this in the case that b(z) has no more than three distinct singularities.

Mathematical Subject Classification

Primary: 12A90

Milestones

Received: 12 February 1971

Published: 1 May 1972