Alexandre Eremenko

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math.CV2026

Holomorphic curves of finite lower order with few inflection points

Alexandre Eremenko, Teng Zhang

We prove a conjecture proposed by the first-named author in 1998. Let $f : C \to P^{n}$ be a transcendental linearly non-degenerate holomorphic curve of finite low…

math.CV2026

A counterexample to Fuchs's conjecture

Alexandre Eremenko, Teng Zhang

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. F…

math.CV2026

The modified Cartan conjecture

Alexandre Eremenko, Zongben Xu, Teng Zhang

In 1928 H. Cartan stated a conjecture about holomorphic curves in $P^{n}$ parametrized by the unit disc, omitting $n + 2$ hyperplanes in general position. He proved it for $n=…