5 papers
Uniform non-homogeneous vector bundles: A counterexample to the conjecture of Drézet and Ballico-Ellia
Graham Denham, Rosa Miró-Roig, Hal Schenck
We construct a rank-9 uniform non-homogeneous vector bundle on . This yields the first counterexample to the longstanding open conjecture that every uniform vector b…
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 be a transcendental linearly non-degenerate holomorphic curve of finite low…
A counterexample to Fuchs's conjecture
Alexandre Eremenko, Teng Zhang
For every in (0, 1/2), we construct an entire function F of order whose logarithmic derivative has zero as a deficient value. This disproves an old conjecture of W. H. J. F…
The modified Cartan conjecture
Alexandre Eremenko, Zongben Xu, Teng Zhang
In 1928 H. Cartan stated a conjecture about holomorphic curves in parametrized by the unit disc, omitting hyperplanes in general position. He proved it for $n=…
High energy eigenfunctions of one-dimensional Schrodinger operators with polynomial potentials
Alexandre Eremenko, Andrei Gabrielov, Boris Shapiro
For a class of one-dimensional Schrodinger operators with polynomial potentials that includes Hermitian and PT-symmetric operators, we show that the zeros of scaled eigenfunctions…