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On the loci |f(z)| = R, f(z) Entire

Published online by Cambridge University Press:  18 May 2009

Dennis A. Hejhal
Dennis A. Hejhal
Affiliation:
University of ChicagoChicago, Ill., U.S.A.
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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.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 10 , Issue 2 , July 1969 , pp. 94 - 102
Copyright
Copyright © Glasgow Mathematical Journal Trust 1969

References

REFERENCES

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