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arXiv · 2609.28443

A counterexample to Fuchs's conjecture

Alexandre Eremenko·Teng Zhang
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Abstract

For every $ρ$ in (0, 1/2), we construct an entire function F of order $ρ$ whose logarithmic derivative has zero as a deficient value. This disproves an old conjecture of W. H. J. Fuchs.

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Alexandre Eremenko, Teng Zhang. 2026-09-23. A counterexample to Fuchs's conjecture. https://arxiv.org/abs/2609.28443

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