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On a Theorem of Tumura and Clunie for a Differential Polynomial

On a Theorem of Tumura and Clunie for a Differential Polynomial ON A THEOREM OF TUMURA AND CLUNIE FOR A DIFFERENTIAL POLYNOMIAL YI HONG XUN 1. Introduction Let /b e a non-constant meromorphic function in the plane. We use with their usual definitions the Nevanlinna functions T{r,f), N(r,f), etc.; S(r,f) is a function, not necessarily the same at each occurrence, that is o(T(r,f)) as r -> oo outside some set of finite linear measure that depends on the context and may be empty. A meromorphic function a(z) that satisfies T(r,a) = S(r,f) is called a 'small' function to / . The notations a = a{z),b,a ,a ... will always denote small with respect 0 lt functions and not just complex constants. n ni (k) k We call M[f] =/ °(/') • • • {f Y , where n ,n ,...,n are non-negative integers, 0 1 k a monomial in / . The integer y = n +... + n is called the degree of the monomial M 0 k and r = n + 2n + ... + (k+\)n is called its weight. If M[f],M[f],...,M[f] M 0 1 k x 2 t denote monomials in / , then is called a differential polynomial in/o f degree y = max{y : http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Wiley

On a Theorem of Tumura and Clunie for a Differential Polynomial

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Publisher
Wiley
Copyright
© London Mathematical Society
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/blms/20.6.593
Publisher site
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Abstract

ON A THEOREM OF TUMURA AND CLUNIE FOR A DIFFERENTIAL POLYNOMIAL YI HONG XUN 1. Introduction Let /b e a non-constant meromorphic function in the plane. We use with their usual definitions the Nevanlinna functions T{r,f), N(r,f), etc.; S(r,f) is a function, not necessarily the same at each occurrence, that is o(T(r,f)) as r -> oo outside some set of finite linear measure that depends on the context and may be empty. A meromorphic function a(z) that satisfies T(r,a) = S(r,f) is called a 'small' function to / . The notations a = a{z),b,a ,a ... will always denote small with respect 0 lt functions and not just complex constants. n ni (k) k We call M[f] =/ °(/') • • • {f Y , where n ,n ,...,n are non-negative integers, 0 1 k a monomial in / . The integer y = n +... + n is called the degree of the monomial M 0 k and r = n + 2n + ... + (k+\)n is called its weight. If M[f],M[f],...,M[f] M 0 1 k x 2 t denote monomials in / , then is called a differential polynomial in/o f degree y = max{y :

Journal

Bulletin of the London Mathematical Society – Wiley

Published: Nov 1, 1988

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