70 citations · 486 across the 82 of their papers we have counts for
5 papers · 1 filter
Nevanlinna functions with real zeros
Alexandre Eremenko, Sergei Merenkov
We show that for every non-negative integer d, there exist differential equations w''+Pw=0, where P is a polynomial of degree d, such that some non-trivial solution w has all zeros…
Meromorphic functions with two completely invariant domains
Walter Bergweiler, Alexandre Eremenko
We show that if a meromorphic function has two completely invariant Fatou components and only finitely many critical and asymptotic values, then its Julia set is a Jordan curve. Ho…
Meromorphic functions with three singular values
Alexandre Eremenko
The minimal possible rate of growth of a meromorphic function with three critical values is found.
Value distribution and potential theory
Alexandre Eremenko
We describe some results of value distribution theory of holomorphic curves and quasiregular maps, which are obtained using potential theory. Among the results discussed are: exten…
Oscillation of Fourier Integrals with a spectral gap
A. Eremenko, D. Novikov
Suppose that Fourier transform of a function f is zero on the interval [-a,a]. We prove that the lower density of sign changes of f is at least a/pi, provided that f is a locally i…