Nevanlinna’s half-plane omitted-values problem

Lineage and corrections

This event attributed to Quanyu Tang

This event attributed to Bokai Cui

This event attributed to Wei He

This event attributed to Tao Hu

This event attributed to Yanyang Li

This event attributed to Ke Wang

This event attributed to Zijun Yu

This event attributed to GPT-5.6 Sol Ultra

ChatGPT prompt evidence for this event

VibeMathed record: Nevanlinna’s half-plane omitted-values problem evidence for this event

Timestamped candidate-proof archive, 24 Aug 2026 (the priority record) evidence for this event

Independent contemporary result by He and Zhang evidence for this event

Eremenko, Kulikov, Sodin - where the problem is explicitly recorded (Question 2) evidence for this event

Nevanlinna’s half-plane omitted-values problem parent of this event

The paper constructs a real meromorphic function $F$ on $\mathbb{C}$ satisfying $F^{-1}(\{0,1,\infty\})\subset\mathbb{R}$, with each of the three fibers $F^{-1}(0)$, $F^{-1}(1)$, and $F^{-1}(\infty)$ infinite, such that for every $a\in\widehat{\mathbb{C}}\setminus\{0,1,\infty\}$, the $a$-point divisor in each of the upper and lower half-planes fails the Blaschke condition. Consequently, $F$ is not of bounded type in either half-plane. This gives a negative answer to Nevanlinna’s century-old question asking whether an entire-plane meromorphic function that omits three distinct values in a half-plane must be of bounded type there. By postcomposition with Möbius transformations, the three exceptional values $\{0,1,\infty\}$ may be replaced by any prescribed triple of distinct values in $\widehat{\mathbb{C}}$. By affine change of variables, the construction applies to any Euclidean half-plane. parent of this event

Nevanlinna’s half-plane omitted-values problem evidence for this event