Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-28T09:34:20.608Z Has data issue: false hasContentIssue false
  • English
  • Français

A NOTE ON THE PERIODICITY OF ENTIRE FUNCTIONS

Part of: Entire and meromorphic functions, and related topics

Published online by Cambridge University Press:  07 February 2019

KAI LIU Open the ORCID record for KAI LIU [Opens in a new window]  and
PEIYONG YU Open the ORCID record for PEIYONG YU [Opens in a new window]
KAI LIU*
Affiliation:
Department of Mathematics,Nanchang University, Nanchang, Jiangxi, 330031, PR China email [email protected], [email protected]
PEIYONG YU
Affiliation:
Department of Mathematics, Nanchang University, Nanchang, Jiangxi, 330031, PR China email [email protected]
*
✉[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.

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.

Keywords

periodic functionentire functionvalue sharing

MSC classification

Primary: 30D35: Distribution of values, Nevanlinna theory
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 100 , Issue 2 , October 2019 , pp. 290 - 296
Copyright
© 2019 Australian Mathematical Publishing Association Inc. 

Footnotes

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).

References

Baker, I. N., ‘On some results of A. Rényi and C. Rényi concerning periodic entire functions’, Acta Sci. Math. (Szeged) 27 (1966), 197–200.Google Scholar
Halburd, R. G., Korhonen, R. J. and Tohge, K., ‘Holomorphic curves with shift-invariant hyperplane preimages’, Trans. Amer. Math. Soc. 366 (2014), 4267–4298.Google Scholar
Hayman, W. K., Meromorphic Functions (Clarendon Press, Oxford, 1964).Google Scholar
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), 352–363.10.1016/j.jmaa.2009.01.053Google Scholar
Laine, I., Nevanlinna Theory and Complex Differential Equations (Walter de Gruyter, Berlin–New York, 1993).Google Scholar
Li, P. and Yang, C. C., ‘Meromorphic solutions of functional equations with nonconstant coefficients’, Proc. Japan Acad. Ser. A 82(2) (2006), 183–186.Google Scholar
Li, S. and Gao, Z. S., ‘A note on the Brück conjecture’, Arch. Math. 95 (2010), 257–268.Google Scholar
Wang, Q. and Hu, P. C., ‘On zeros and periodicity of entire functions’, Acta Math. Sci. 38(2) (2018), 209–214.Google Scholar
Yang, C. C., ‘A generalization of a theorem of P. Montel on entire functions’, Proc. Amer. Math. Soc. 26 (1970), 332–334.10.1090/S0002-9939-1970-0264080-XGoogle Scholar
Yang, C. C., ‘On periodicity of entire functions’, Proc. Amer. Math. Soc. 43 (1974), 353–356.10.1090/S0002-9939-1974-0333180-1Google Scholar
Yang, C. C. and Hua, X. H., ‘Unique polynomials of entire and meromorphic functions’, Mat. Fiz. Anal. Geom. 4 (1997), 391–398.Google Scholar
Yang, C. C. and Yi, H. X., Uniqueness Theory of Meromorphic Functions (Kluwer, Dordrecht, 2003).10.1007/978-94-017-3626-8Google Scholar