PreprintarXiv licencearXiv
Three omitted values and non-Blaschke point divisors in half-planes
Abstract
We construct a real meromorphic function F on ℂ such that F−1({0,1,∞})⊂ℝ, while F is not of bounded type in either half-plane. More strongly, for every a∈ℂ̂∖{0,1,∞}, the a-point divisor in either half-plane fails the Blaschke condition. Thus the construction gives a negative answer to the half-plane bounded-type question arising from Nevanlinna's 1925 work. Postcomposition gives the analogous counterexample for any prescribed triple of distinct values in the Riemann sphere. The core construction and proof were generated during an autonomous run of GPT-5.6 Sol Ultra.
Related
- The range and omitted values of a certain sequence involving the partition function
- An Improved Lower Bound for the Three-Dimensional Blaschke--Lebesgue Problem from Spectral and Dual Perspectives
- A 0.41275 lower bound for the three-dimensional Blaschke-Lebesgue problem
- Explicit equations of three pairs of fake projective planes
- Unsupported Cyclotomic Divisors in Three-Prime Integer Tilings
BibTeX
@misc{tang2026three,
title = {{Three omitted values and non-Blaschke point divisors in half-planes}},
author = {Quanyu Tang and Bokai Cui and Wei He and Tao Hu and Yanyang Li and Ke Wang and Zijun Yu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.26062},
eprint = {2608.26062},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.26062},
}
RIS
TY - UNPB
TI - Three omitted values and non-Blaschke point divisors in half-planes
AU - Quanyu Tang
AU - Bokai Cui
AU - Wei He
AU - Tao Hu
AU - Yanyang Li
AU - Ke Wang
AU - Zijun Yu
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2608.26062
UR - https://arxiv.org/abs/2608.26062
AB - We construct a real meromorphic function F on ℂ such that F^−1({0,1,∞})⊂ℝ, while F is not of bounded type in either half-plane. More strongly, for every a∈ℂ̂∖{0,1,∞}, the a-point divisor in either half-plane fails the Blaschke condition. Thus the construction gives a negative answer to the half-plane bounded-type question arising from Nevanlinna's 1925 work. Postcomposition gives the analogous counterexample for any prescribed triple of distinct values in the Riemann sphere. The core construction and proof were generated during an autonomous run of GPT-5.6 Sol Ultra.
ER -