Variations on a Conjecture of C. C. Yang Concerning Periodicity
2021
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.
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