Four-value CM conjecture for infinite-order meromorphic functions
Four-value CM conjecture for infinite-order meromorphic functions
Let and be two distinct transcendental meromorphic functions of infinite order, and let be four distinct values in the extended complex plane. Four-value CM conjecture. If and share IM and CM, then they share all four values CM. This extends the corresponding finite-order result and asks whether the weaker IM/CM sharing hypothesis forces complete CM sharing in the infinite-order case.
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Primary source
Xiao-Min Li, Qing-Fei Zhai and Hong-Xun Yi, “On a question of Gary G. Gundersen concerning meromorphic functions sharing three distinct values IM and a fourth value CM”, arXiv:2402.03248 (2026).
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