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A NOTE ON THE PERIODICITY OF ENTIRE FUNCTIONS

  • KAI LIU (a1) and PEIYONG YU (a2)
Abstract

We give some sufficient conditions for the periodicity of entire functions based on a conjecture of C. C. Yang, using the concepts of value sharing, unique polynomial of entire functions and Picard exceptional value.

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This work was partially supported by the NSFC (No. 11661052), the NSF of Jiangxi (No. 20161BAB211005) and the outstanding youth scientist foundation plan of Jiangxi (No. 20171BCB23003).

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[1] Baker, I. N., ‘On some results of A. Rényi and C. Rényi concerning periodic entire functions’, Acta Sci. Math. (Szeged) 27 (1966), 197200.
[2] Halburd, R. G., Korhonen, R. J. and Tohge, K., ‘Holomorphic curves with shift-invariant hyperplane preimages’, Trans. Amer. Math. Soc. 366 (2014), 42674298.
[3] Hayman, W. K., Meromorphic Functions (Clarendon Press, Oxford, 1964).
[4] Heittokangas, J., Korhonen, R., Laine, I., Rieppo, J. and Zhang, J. L., ‘Value sharing results for shifts of meromorphic functions, and sufficient conditions for periodicity’, J. Math. Anal. Appl. 355 (2009), 352363.
[5] Laine, I., Nevanlinna Theory and Complex Differential Equations (Walter de Gruyter, Berlin–New York, 1993).
[6] Li, P. and Yang, C. C., ‘Meromorphic solutions of functional equations with nonconstant coefficients’, Proc. Japan Acad. Ser. A 82(2) (2006), 183186.
[7] Li, S. and Gao, Z. S., ‘A note on the Brück conjecture’, Arch. Math. 95 (2010), 257268.
[8] Wang, Q. and Hu, P. C., ‘On zeros and periodicity of entire functions’, Acta Math. Sci. 38(2) (2018), 209214.
[9] Yang, C. C., ‘A generalization of a theorem of P. Montel on entire functions’, Proc. Amer. Math. Soc. 26 (1970), 332334.
[10] Yang, C. C., ‘On periodicity of entire functions’, Proc. Amer. Math. Soc. 43 (1974), 353356.
[11] Yang, C. C. and Hua, X. H., ‘Unique polynomials of entire and meromorphic functions’, Mat. Fiz. Anal. Geom. 4 (1997), 391398.
[12] Yang, C. C. and Yi, H. X., Uniqueness Theory of Meromorphic Functions (Kluwer, Dordrecht, 2003).
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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