Four-value CM conjecture for infinite-order meromorphic functions

Let ff and gg be two distinct transcendental meromorphic functions of infinite order, and let a1,a2,a3,a4a_1,a_2,a_3,a_4 be four distinct values in the extended complex plane. Four-value CM conjecture. If ff and gg share a1,a2,a3a_1,a_2,a_3 IM and a4a_4 CM, then they share all four values a1,a2,a3,a4a_1,a_2,a_3,a_4 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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