The generalized Yang’s Conjecture states that if, given an entire function f(z) and positive integers n and k, \(f(z)^nf^{(k)}(z)\) is a periodic function, then f(z) is also a periodic function. In this paper, it is shown that the generalized Yang’s conjecture is true for meromorphic functions in the case \(k=1\). When \(k\ge 2\) the conjecture is shown to be true under certain conditions even if n is allowed to have negative integer values.

中文翻译：

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杨洋关于周期性的猜想的变化

广义杨氏猜想指出，如果给定整个函数f（z）和正整数n和k，\（f（z）^ nf ^ {（k）}（z）\）是周期函数，则f（z）也是一个周期函数。在本文中，证明了对于\（k = 1 \）情况下的亚纯函数，广义Yang猜想是正确的。当\（k \ ge 2 \）时，即使允许n具有负整数值，在某些条件下该猜想也显示为真。