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On the deficiencies of composite entire functions

Published online by Cambridge University Press:  20 January 2009

J. K. Langley
J. K. Langley
Affiliation:
Department of MathematicsUniversity of NottinghamNottingham NG7 2RD
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Abstract

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For any sequence (aj) of complex numbers and for any ρ > ½, we construct an entire function F with the following properties. F has order ρ, mean type, each aj is a deficient value of F, and F is given by F(z)=f(g(z)), where f and g are transcendental entire functions. This complements a result of Goldstein. We also construct, for any ρ>½, an entire function G of order p, mean type, such that liminf,→ ∞ T(r, G)/T(r, G′)>1.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 36 , Issue 1 , February 1993 , pp. 151 - 164
Copyright
Copyright © Edinburgh Mathematical Society 1993

References

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