整函数与其差分或平移分担一个小函数
Entire Functions Sharing a Small Function with Its Difference Operators or Shifts
摘要: 本文研究有穷级整函数 与其差分算子 或移位算子 计数分担一小函数 的唯一性问题。得到两个重要结论：如果 和 计数分担 ，则 。如果 和 计数分担 ，则 或 。这些结论推广了李昇和高宗升在[1]中的结论。
Abstract: In this paper, we investigate an entire function of finite order share a small function with its difference and shift. Two theorems will be got, that is, if and share CM (counting multiplies), then ; if and share CM, then or . The results we obtain improve some known results of Li Sheng and Gao Zongsheng in [1].
文章引用：李秋颖, 申田田, 王庆泉. 整函数与其差分或平移分担一个小函数[J]. 理论数学, 2011, 1(3): 205-207. http://dx.doi.org/10.12677/pm.2011.13039

参考文献

[1] S. Li, Z. S. Gao. A note on the Bruck conjecture. Archiv Der Mathematik, 2010, 95(3): 257-268.
[2] W. Hayman. Meromorphic function. Oxford: Clarendon Press, 1964.
[3] I. Laine. Nevanlinna theory and complex differential equation. Berlin: Walter de Gruyter, 1993.
[4] 杨乐. 值分布论及其新研究[M]. 北京: 科学出版社, 1982.
[5] 仪洪勋, 杨重骏. 亚纯函数唯一性理论[M]. 北京: 科学出版社, 1995.
[6] L. A. Rubel, C. C. Yang. Values shared by an entire function and its derivative. Complex Analysis, Lecture Notes in Math, 1977, 599: 101-103.
[7] Y.-M. Chiang, S.-J. Feng. On the Nevanlinna characteristic of and difference equations in the complex plane. The Ramanujan Journal, 2008, 16(1): 105-129.
[8] Y.-M. Chiang, S.-J. Feng. On the growth of logarithmic differences, difference quotients and logarithmic derivatives of meromorphic functions. Transaction of American Mathematical Society, 2009, 361(7): 3767-3791.
[9] R. G. Halburd, R. J. Korhonen. Nevanlinna theory for the difference operator. Annals Academy Scientiarum Fennicy Mathematical, 2006; 31(2): 463-478.
[10] R. G. Halburd, R. J. Korhonen. Difference analogue of the lemma on the logarithmic derivative with applications to difference equations. Journal of Mathematical Analysis and Applications, 2006, 314(2): 477-487.
[11] J. Heittokangas, R. Korhonen, I. Laine, J. Rieppo and J. L. Zhang. Value sharing results for shifts of meromorphic functions, and sufficient conditions for periodicity. Journal of Mathematical Analysis and Applications, 2009, 355(1): 352-363.
[12] W. Bergweiler, J. K. Langley. Zeros of differences of meromorphic functions. Mathematical Proceedings of the Cambridge Philosophical Society, 2007, 142: 133-147.
[13] J. Wang. Growth and poles of meromorphic solutions of some difference equations. Journal of Mathematical Analysis and Applications, 2011, 379: 367- 377.

为你推荐