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On the common right factors of meromorphic functions

Published online by Cambridge University Press:  17 April 2009

Tuen-Wai Ng  and
Chung-Chun Yang
Tuen-Wai Ng
Affiliation:
Department of Mathematics, Hong King University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, e-mail: [email protected]
Chung-Chun Yang
Affiliation:
Department of Mathematics, Hong King University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, e-mail: [email protected]
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In this paper, common right factors (in the sense of composition) of p1 + p2F and p3 + p4F are investigated. Here, F is a transcendental meromorphic function and pi's are non-zero polynomials. Moreover, we also prove that the quotient (p1 + p2F)/(p3 + p4F) is pseudo-prime under some restrictions on F and the pi's. As an application of our results, we have proved that R (z) H (z)is pseudo-prime for any nonconstant rational function R (z) and finite order periodic entire function H (z).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 55 , Issue 3 , June 1997 , pp. 395 - 403
Copyright
Copyright © Australian Mathematical Society 1997

References

[1]Bergweiler, W., ‘On the composition of transcendental entire and meromorphic functions’, Proc. Amer. Math. Soc. 123 (1995), 2151–2153.CrossRefGoogle Scholar
[2]Bergweiler, W. and Yang, C.C., ‘On the value distribution of composite meromorphic functions’, Bull. London Math. Soc. 25 (1993), 357–361.CrossRefGoogle Scholar
[3]Edrei, A. and Fuchs, W.H.J., ‘On the zeros of f (g (z)) where f and g are entire functions’, J. Analyse Math. 12 (1964), 243–255.CrossRefGoogle Scholar
[4]Gross, F., ‘On factorization of meromorphic fucntions’, Trans. Amer. Math. Soc. 131 (1968), 215–222.CrossRefGoogle Scholar
[5]Gross, F. and Osgood, C.F., ‘A simpler proof of a theorem of Steinmetz’, J. Math. Anal. Appl. 142 (1989), 290–294.CrossRefGoogle Scholar
[6]Gross, F. and Osgood, C.F., ‘An extension of a theorem of Steinmetz’, J. Math. Anal. Appl. 159 (1991), 287–292.CrossRefGoogle Scholar
[7]Hayman, W.K., Meromorphic functions (Clarendon Press, Oxford, 1964).Google Scholar
[8]Mohon'ko, A.Z., ‘The Nevanlinna characteristics of certain meromorphic functions’, (in Russian), Teor. Funktsií Funktsional. Anal. i Prilozhen. 14 (1971), 83–87.Google Scholar
[9]Steinmetz, N., ‘Über die faktorisierbaren Losungen Gewohnlicher differentialgleichungen’, Math. Z. 170 (1980), 169–180.CrossRefGoogle Scholar
[10]Urabe, H., ‘Some remarks on factorization of meromorphic functions of finite order with a finite number of poles’, Bull. Kyoto Univ. Ed. Ser. B 83 (1993), 1–7.Google Scholar
[12]Zheng, J.H., ‘On permutability of periodic entire functions’, J. Math. Anal. Appl. 140 (1989), 262–269.CrossRefGoogle Scholar