Value sharing results for shifts of meromorphic functions, and sufficient conditions for periodicity
Value sharing results for shifts of meromorphic functions, and sufficient conditions for periodicity
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DOI：
10.1016/j.jmaa.2009.01.053
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发表时间：
2009-07-01
影响因子：
1.3
通讯作者：
Zhang, J.
中科院分区：
文献类型：
--
作者：
Heittokangas, J.;Korhonen, R.;Zhang, J.
这项研究是前四位作者最近发表的一篇论文的延续。研究了亚纯函数f（z）及其移位f（z + c）的分担值问题，其中C是C的元素.例如，证明了：如果f（z）是有限阶的，且与它的移位f（z + c）有两个CM和一个IM值，则f是周期为c的周期函数。如果f在不同的方向上有两个位移，那么关于f的阶的假设就可以被放弃，这就导致了一种新的刻画椭圆函数的方法。研究结果还包括一个类似的位移著名的猜想布鲁克关于价值共享的整个函数f与其衍生物f '。(C)2009 Elsevier Inc. All rights reserved.
This research is a continuation of a recent paper due to the first four authors. Shared value problems related to a meromorphic function f(z) and its shift f(z + c), where C is an element of C, are studied. It is shown, for instance, that if f(z) is of finite order and shares two values CM and one value IM with its shift f(z + c), then f is a periodic function with period c. The assumption on the order of f can be dropped if f shares two shifts in different directions, leading to a new way of characterizing elliptic functions. The research findings also include an analogue for shifts of a well-known conjecture by Bruck concerning the value sharing of an entire function f with its derivative f'. (C) 2009 Elsevier Inc. All rights reserved.