Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-23T14:54:00.531Z Has data issue: false hasContentIssue false

On Uniqueness of Meromorphic Functions with Shared Values in Some Angular Domains

Published online by Cambridge University Press:  20 November 2018

Zheng Jian-Hua*
Affiliation:
Department of Mathematical Sciences Tsinghua University Beijing 100084 China, email: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we investigate the uniqueness of transcendental meromorphic function dealing with the shared values in some angular domains instead of the whole complex plane.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2004

References

[1] Baernstein, A., Proof of Edrei's spread conjecture. Proc. London Math. Soc. 26 (1973), 418434.Google Scholar
[2] Baker, I. N., Sets of non-normality in iteration theory. J. London Math. Soc. 40 (1965), 499502.Google Scholar
[3] Baker, I. N., Kotus, J. and , Y., Iterates of meromorphic functions: I. Ergodic Theory Dynamical Systems 11 (1991), 241248.Google Scholar
[4] Bergweiler, W., Iteration of meromorphic functions. Bull. Amer.Math. Soc. (N.S.) 29 (1993), 151188.Google Scholar
[5] Cebotarev, N. G., Ueber die Realit¨at von Nullstellen ganzer transzendenten Funktionen. Math. Ann. 99 (1928), 660686.Google Scholar
[6] Edrei, A., Meromorphic functions with three radially distributed values. Trans. Amer.Math. Soc. 78 (1955), 276293.Google Scholar
[7] Edrei, A., Sums of deficiencies of meromorphic functions. J. AnalyseMath. 14 (1965), 79107.Google Scholar
[8] Frank, G. and Schwick, W., Meromorphe Funktionen, die mit einer Ableitung drei Werte teilen. Results Math. 22 (1992), 679684.Google Scholar
[9] Hayman, W. K., Meromorphic functions. Oxford, 1964.Google Scholar
[10] Goldberg, A. A. and Ostrovskii, I. V., The distribution of values of meromorphic functions. (Russian) Izdat. Nauka, Moscow, 1970.Google Scholar
[11] Levin, B. Ya., Distribution of zeros of entire functions. (Russian original, Moscow, 1956) Transl. Math. Monographs 5, American Mathematical Society, Providence, 1964.Google Scholar
[12] Nevanlinna, R., Le théorème de Picard-Borel et la théorie des fonctions méromorphes. Paris, 1929.Google Scholar
[13] Yang, L., Borel directions of meromorphic functions in an angular domain. Sci. Sinica 1979, 149163.Google Scholar
[14] Yang, L. and Yang, C.-C. Angular distribution of values of f f′. Science in China, 37 (1994), 284294.Google Scholar
[15] Zheng, J. H., On the growth of meromorphic functions with two radially distributed values. J. Math. Anal. Appl. 206 (1997), 140154.Google Scholar
[16] Zheng, J. H., On transcendental meromorphic functions with radially distributed values. Science in China, to appear.Google Scholar