Abstract
In this paper, we first discuss a class of meromorphic functions satisfying a certain property on characteristic functions of Nevanlinna theory and then give the applications of the class to Yang’s conjecture and its variants.
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Chen, Y.Y., Long, F., Wang, J.: On entire solutions of some non-linear differential equations (submitted)
Chen, Z.X.: Growth and zeros of meromorphic solution of some linear difference equations. J. Math. Anal. Appl. 373, 235–241 (2011)
Chen, Z.X.: On properties of meromorphic solutions for difference equations concerning gamma function. J. Math. Anal. Appl. 406, 147–157 (2013)
Chiang, Y.M., Feng, S.J.: On the Nevanlinna characteristic of \(f(z+\eta )\) and difference equations in the complex plane. Ramanujan J. 16, 105–129 (2008)
Gross, F.: Factorization of Meromorphic Functions. U. S. Gov. Printing Office, Washington, DC (1972)
Gundersen, G.G., Lü, W.R., Ng, T.W., Yang, C.C.: Entire solutions of differential equations that are related to trigonometric identities. J. Math. Anal. Appl. 507(1), 125788 (2022)
Halburd, R.G., Korhonen, R.J., Tohge, K.: Holomorphic curves with shift-invariant hyperplane preimages. Trans. Am. Math. Soc. 366, 4267–4298 (2014)
Hayman, W.K.: Meromorphic Functions. Clarendon Press, Oxford (1964)
Heittokangas, J., Ishizaki, K., Tohge, K., Wen, Z.T.: Value distribution of exponential polynomials and their role in the theories of complex differential equations and oscillation theory. Bull. Lond. Math. Soc. 366, 1–77 (2023)
Ishizaki, K.: Meromorphic solutions of difference Riccati equations. Complex Var. Ellipt. Equ. 62, 110–122 (2017)
Laine, I.: Nevanlinna Theory and Complex Differential Equations. Walter de Gruyter, Berlin (1993)
Latreuch, Z., Zemirni, M.A.: On a theorem of A. and C. Rényi and a conjecutre of C. C. Yang concerning periodicity of entire functions. Anal. Math. 48, 111–125 (2022)
Li, P., Lü, W.R., Yang, C.C.: Entire solutions of certain types of nonlinear differential equations. Houst. J. Math. 45(2), 431–437 (2019)
Liu, K., Laine, I., Yang, L.Z.: Complex Delay-Differential Equations. De Gruyter, Boston (2021)
Liu, K., Wei, Y.M., Yu, P.Y.: Generalized Yang’s Conjecture on the periodicity of entire functions. Bull. Korean Math. Soc. 57(5), 1259–1267 (2020)
Liu, K., Yu, P.Y.: A note on the periodicity of entire functions. Bull. Aust. Math. Soc. 100(2), 290–296 (2019)
Liu, X. L.: The periodicity of transcendental meromorphic functions. Publications Univ. Eastern Finland, Diss. Forestry and Natural Sci. 419 (2021)
Liu, X.L., Korhonen, R.: The periodicity of transcendental entire functions. Bull. Aust. Math. Soc. 101(3), 453–465 (2020)
Liu, X.L., Korhonen, R., Liu, K.: Variations on a conjecture of C. C. Yang concerning periodicity. Comput. Methods Funct. Theory 22, 27–33 (2022)
Liu, X.L., Liu, K., Korhonen, R.: Inverse problems on the parity of meromorphic functions. J. Math. Anal. Appl. 512(1), 126129 (2022)
Lü, W.R., Zhang, X.X.: On the periodicity of entire functions. Results Math. 75, 176 (2020)
Milloux, H.: Les fonctions méromorphes et leurs dérivées, Pairs (1940)
Steinmetz, N.: Zur Wertverteilung der quotienten von exponentialpolynomen. Arch. Math. (Basel) 35, 461–470 (1980)
Wang, Q., Hu, P.C.: On zeros and periodicity of entire functions. Acta Math. Sci. 38(2), 209–214 (2018)
Yang, C.C., Yi, H.X.: Uniqueness Theory of Meromorphic Functions. Kluwer Academic Publishers, Dordrecht (2003)
Yang, C.C.: Value distribution theory and its applications to functional equations. In: The third Russian-Chinese conference on complex analysis, algebra, algebraic geometry and mathematical physics. Steklov Mathematical Institute of RAS, Moscow (2016). http://www.mathnet.ru/eng/conf800
Zemirni, M.A., Laine, I., Latreuch, Z.: New findings on the periodicity of entire functions and their differential polynomials. Mediterr. J. Math. 20, 136 (2023)
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There is only one author, Xinling Liu wrote and reviewed the manuscript.
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This work was supported by National Natural Science Foundation of China (No. 12061042, 12061041).
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Liu, X. A Class of Meromorphic Functions with Yang’s Conjecture Concerning Periodicity. Mediterr. J. Math. 21, 82 (2024). https://doi.org/10.1007/s00009-024-02627-y
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DOI: https://doi.org/10.1007/s00009-024-02627-y