JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (2): 1-8.doi: 10.6040/j.issn.1671-9352.0.2019.474

   

Uniqueness of meromorphic functions sharing four distinct finite values with L-functions

LI Xiao-min, WU Cong-cong*   

  1. School of Mathematical Science, Ocean University of China, Qingdao 266100, Shandong, China
  • Published:2020-02-14

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Abstract: This paper studies a uniqueness question of a nonconstant meromorphic function f sharing three distinct finite values IM and a fourth finite value CM with an L-function L belonging to the extended Selberg class. The main result obtained in this paper improves and extends many known results.

Key words: Nevanlinnas theory, meromorphic function, L-function, uniqueness theorem

CLC Number: 

  • O174.52
[1] HAYMAN W K. Meromorphic functions[M]. Oxford: Clarendon Press, 1964: 7.
[2] YANG Lo. Value distribution theory[M]. Berlin: Springer-Verlag, 1993.
[3] 仪洪勋,杨重骏. 亚纯函数的唯一性理论[M]. 北京:科学出版社,1995. YI Hongxun, YANG Chungchun. Uniqueness theory of meromorphic functions[M]. Beijing: Science Press, 1995.
[4] LI Xiaomin, YI Hongxun. Results on value distribution of L-functions[J]. Mathematische Nachrichten, 2013, 286(13):1326-1336.
[5] GUNDERSEN G G. Meromorphic functions that share three values IM and a fourth value CM[J]. Complex Variables and Elliptic Equations, 1992, 20(1/2/3/4):99-106.
[6] STEUDING J. Value distribution of L-functions[M]. Berlin: Springer-Verlag, 2007: 150.
[7] LI Baoqin. A result on value distribution of L-functions[J]. Proceedings of the American Mathematical Society, 2010, 138(6):2071-2077.
[8] MOKHONKO A Z. The Nevanlinna characteristics of certain meromorphic functions[J]. Teoriya Funktsiǐ, Funktsionalnyǐ Analiz i ikh Prilozheniya, 1971, 14:83-87.(Russian)
[9] NEVANLINNA R. Einige eindeutigkeitssätze in der theorie der meromorphen funktionen[J]. Acta Mathematica, 1926, 48(3/4):367-391.
[10] GUNDERSEN G G. Meromorphic functions that share four values[J]. Transactions of the American Mathematical Society, 1983, 277(2):545-567. Correction: 1987, 304(2):847-850.
[11] LI Xiaomin, YI Hongxun. Meromorphic functions sharing four values[J]. Proceedings of the Japan Academy, Series A, Mathematical Sciences, 2007, 83(7):123-128.
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[15] LIU Shu-kuan. The normality criteria about f+a(z)(f ′)n [J]. J4, 2011, 46(1): 79-80.
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