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

Abstract

AbstractThe generalized Yang’s Conjecture states that if, given an entire function f(z) and positive integers n and k, $$f(z)^nf^{(k)}(z)$$ f ( z ) n f ( 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 $$k=1$$ k = 1 . When $$k\ge 2$$ k ≥ 2 the conjecture is shown to be true under certain conditions even if n is allowed to have negative integer values.