Vol. 41, No. 2, 1972

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

David Geoffrey Cantor

Vol. 41 (1972), No. 2, 329–334

Suppose an,bn, and cn = anbn are sequences of algebraic integers and that all bn are nonzero. It is easy to verify that if both a(z) = n=0anzn and b(z) = n=0bnzn are rational functions, then so is c(z) = n=0cnzn. 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
Received: 12 February 1971
Published: 1 May 1972
David Geoffrey Cantor