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An entire function that violates quasiminimality
Abstract
Zilber's celebrated quasiminimality conjecture states that a subset of ℂ defined by polynomials and exponentials is either countable, or has countable complement. Koiran has asked whether the same could be true replacing exp with any unary entire function. We give a negative answer to Koiran's question, using results from the theory of holomorphic approximation.
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BibTeX
@misc{dembner2026entire,
title = {{An entire function that violates quasiminimality}},
author = {Spencer Dembner},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08071},
eprint = {2610.08071},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08071},
}
RIS
TY - UNPB
TI - An entire function that violates quasiminimality
AU - Spencer Dembner
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.08071
UR - https://arxiv.org/abs/2610.08071
AB - Zilber's celebrated quasiminimality conjecture states that a subset of ℂ defined by polynomials and exponentials is either countable, or has countable complement. Koiran has asked whether the same could be true replacing exp with any unary entire function. We give a negative answer to Koiran's question, using results from the theory of holomorphic approximation.
ER -