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On the loci |f(z)| = R, f(z) Entire
Published online by Cambridge University Press: 18 May 2009
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The following result is found quite widely. Suppose f(z) is a non-constant entire function such that |f(z)| = 1 along |z| = 1. Then, f (z) has form czm, |c| = 1, m ≧ 1. See Ahlfors [1, p. 172, exercise 3], Dienes [4, p. 172, exercise 23], Hille [6, p. 317, exercise 2]. It is natural to inquire about a generalization of this result.
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- Copyright © Glasgow Mathematical Journal Trust 1969
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