QUASIPERIODICITY OF TRANSCENDENTAL MEROMORPHIC FUNCTIONS*

  • Xinling LIU ,
  • Kai Liu ,
  • Risto Korhonen ,
  • Galina Filipuk
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  • 1. Department of Mathematics, Nanchang University, Nanchang 330031, China;
    2. Department of Physics and Mathematics, University of Eastern Finland, P. O. Box 111, 80101, Joensuu, Finland;
    3. Department of Mathematics, Nanchang University, Nanchang 330031, China;
    4. Department of Physics and Mathematics, University of Eastern Finland, P. O. Box 111, 80101, Joensuu, Finland;
    5. Institute of Mathematics, Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2,02-097, Warsaw, Poland
Xinling LIU, E-mail: liuxinling@ncu.edu.cn; Kai Liu, E-mail: liukai@ncu.edu.cn; Galina Filipuk, E-mail: G.filipuk@uw.edu.pl

Received date: 2022-10-11

  Online published: 2024-02-27

Supported by

The first author and the second author's researches were partially supported by the NSFC (12061042) and the NSF of Jiangxi (20202BAB201003). GF acknowledges the support of the National Science Center (Poland) via grant 2017/25/B/ST1/00931. The work of the GF was also partially supported by the Project PID2021-124472NB-I00 funded by MCIN/AEI/10.13039/501100011033 and by "EFDF A way of making Europe"

Abstract

This paper is devoted to considering the quasiperiodicity of complex differential polynomials, complex difference polynomials and complex delay-differential polynomials of certain types, and to studying the similarities and differences of quasiperiodicity compared to the corresponding properties of periodicity.

Cite this article

Xinling LIU , Kai Liu , Risto Korhonen , Galina Filipuk . QUASIPERIODICITY OF TRANSCENDENTAL MEROMORPHIC FUNCTIONS*[J]. Acta mathematica scientia, Series B, 2024 , 44(1) : 161 -172 . DOI: 10.1007/s10473-024-0108-0

References

[1] Cherry W, Ye Z.Nevanlinna's Theory of Value Distribution. Berlin: Springer-Verlag, 2001
[2] Chuang C T, Yang C C.Fix Points and Factorization of Meromorphic Functions. Singapore: World Scientific Publ Co, 1990
[3] Halburd R G, Korhonen R J, Tohge K. Holomorphic curves with shift-invariant hyperplane preimages. Trans Amer Math Soc, 2014, 366: 4267-4298
[4] Hayman W K. Meromorphic Functions.Oxford: Clarendon Press, 1964
[5] Kohno M.Global Analysis in Linear Differential Equations. Mathematics and Its Applications 471. Dordrecht: Kluwer Academic Publishers, 1999
[6] Laine I.Nevanlinna Theory and Complex Differential Equations. Berlin-New York: Walter de Gruyter, 1993
[7] Li P, Lü W R, Yang C C. Entire solutions of certain types of nonlinear differential equations. Houston J Math, 2019, 45(2): 431-437
[8] Liu K, Yu P Y. A note on the periodicity of entire functions. Bull Aust Math Soc, 2019, 100(2): 290-296
[9] Liu K, Liu X L, Yang L Z. The zero distribution and uniqueness of difference-differential polynomials. Ann Polon Math, 2013, 109: 137-152
[10] Liu K, Wei Y M, Yu P Y. Generalized Yang's Conjecture on the periodicity of entire functions. Bull Korean Math Soc, 2020, 57(5): 1259-1267
[11] Liu K, Laine I, Yang L Z.Complex Delay-Differential Equations. Berlin, Boston: De Gruyter, 2021
[12] Liu X L, Korhonen R. The periodicity of transcendental entire functions. Bull Aust Math Soc, 2020, 101(3): 453-465
[13] Liu X L, Korhonen R, Liu K. Variations on a conjecture of C. C. Yang concerning periodicity. Comput Methods Funct Theory, 2022, 22: 27-33
[14] Liu X L.The Periodicity of Transcendental meromorphic Functions[D]. Joensuu: Univ Eastern Finland, 2021
[15] Ozawa M. On the existence of prime periodic entire functions. Ködai Math Sem Rep, 1977/78, 29: 308-321
[16] Rényi A, Rényi C. Some remarks on periodic entire functions. J Analyse Math, 1965, 14(1): 303-310
[17] Wang Q, Hu P C. On zeros and periodicity of entire functions. Acta Math Sci, 2018, 38A(2): 209-214
[18] Wei Y M, Liu K, Liu X L. The periodicity on a transcendental entire function with its differential polynomials. Analysis Math, 2021, 47: 695-708
[19] Yamanoi K. The second main theorem for small functions and related problems. Acta Math, 2004, 192: 225-294
[20] Yang C C, Yi H X.Uniqueness Theory of Meromorphic Functions. Dordrecht: Kluwer Academic Publishers, 2003
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