Uniqueness of meromorphic functions sharing values with their shifts
Uniqueness of meromorphic functions sharing values with their shifts
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DOI：
10.1080/17476930903394770
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发表时间：
2011-01
影响因子：
0.9
通讯作者：
J. Heittokangas;R. Korhonen;I. Laine;J. Rieppo
中科院分区：
文献类型：
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作者：
J. Heittokangas;R. Korhonen;I. Laine;J. Rieppo
研究了一类亚纯函数f (z)及其位移f （z + c）的共享值问题，其中c∈。例如，如果f (z)是有限阶的，并且与它的移位f （z + c）共享至少三个计数多重值，则f是一个周期为c的周期函数。如果f在不同方向上共享两次移位，则可以放弃对f阶的假设。更准确地说，证明了如果c1和c2是实数上线性无关的复常数，并且f (z)是与移位函数f （z + c1）和f （z + c2）共享三个计数多重值的任意非常数亚纯函数，则f是周期为c1和c2的椭圆函数。这可以看作是表征椭圆函数的一种新方法。
Shared value problems related to a meromorphic function f (z) and its shift f (z + c), where c ∈ ℂ, are studied. It is shown, for instance, that if f (z) is of finite order and shares at least three values counting multiplicities 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. More precisely, it is proved that if c 1 and c 2 are complex constants which are linearly independent over the real numbers, and f (z) is any non-constant meromorphic function sharing three values counting multiplicities with the shifted functions f (z + c 1) and f (z + c 2), then f is an elliptic function with periods c 1 and c 2. This can be seen as a new way of characterizing elliptic functions.