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Unavoidable systems of functions

Published online by Cambridge University Press:  24 October 2008

W. K. Hayman  and
Lee A. Rubel
W. K. Hayman
Affiliation:
Department of Mathematics, University of York, Heslington, York YO1 5DD, U.K.
Lee A. Rubel
Affiliation:
Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, Illinois 61801, U.S.A.
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Extract

Suppose that D is a plane domain and that f(z), g(z) are meromorphic in D and f(z) ╪ g(z) for all z in D. Then following Rubel and Yang [11], we say that f(z) avoids g(z) in D. A system of functions g1(z), …, gn(z) is said to be unavoidable if, whenever f is meromorphic in D, at least one of the equations f(z) = gv(z) has a root in D. Rubel and Yang [11] proved that if D is the open plane, then any two functions form an avoidable system, but three distinct polynomials a1, a2, a3 such that a1−a2 and a2−a3 are not both constant form an unavoidable system.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 117 , Issue 2 , March 1995 , pp. 345 - 351
Copyright
Copyright © Cambridge Philosophical Society 1995

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References

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