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Proof of a conditional theorem of Littlewood on the distribution of values of entire functions
A. È. Eremenko, M. L. Sodin
It is proved that for any entire function $f$ of finite nonzero order there is a set $S$ in the plane with density zero and such that for any $a\in\mathbf C$ almost all the roots of the equation $f(z)=a$ belong to $S$. This assertion was deduced by Littlewood from an unproved conjecture about an estimate of the spherical derivative of a polynomial. This conjecture is proved here in a weakened form.
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Mathematics of the USSR-Izvestiya, 1988, 30:2, 395–402
MSC: Primary 30D35; Secondary 30C10
A. È. Eremenko, M. L. Sodin, “Proof of a conditional theorem of Littlewood on the distribution of values of entire functions”, Izv. Akad. Nauk SSSR Ser. Mat., 51:2 (1987), 421–428; Math. USSR-Izv., 30:2 (1988), 395–402
Citation in format AMSBIB
\by A.~\`E.~Eremenko, M.~L.~Sodin
\paper Proof of a~conditional theorem of Littlewood on the distribution of values of entire functions
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\jour Math. USSR-Izv.
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John L. Lewis, “On a conditional theorem of Littlewood for quasiregular entire functions”, J Anal Math, 62:1 (1994), 169
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