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 Izv. Akad. Nauk SSSR Ser. Mat., 1987, Volume 51, Issue 2, Pages 421–428 (Mi izv1302)

Proof of a conditional theorem of Littlewood on the distribution of values of entire functions

A. È. Eremenko, M. L. Sodin

Abstract: 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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English version:
Mathematics of the USSR-Izvestiya, 1988, 30:2, 395–402

Bibliographic databases:

UDC: 517.53
MSC: Primary 30D35; Secondary 30C10

Citation: 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
\Bibitem{EreSod87} \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. \yr 1987 \vol 51 \issue 2 \pages 421--428 \mathnet{http://mi.mathnet.ru/izv1302} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=897006} \zmath{https://zbmath.org/?q=an:0638.30029|0627.30025} \transl \jour Math. USSR-Izv. \yr 1988 \vol 30 \issue 2 \pages 395--402 \crossref{https://doi.org/10.1070/IM1988v030n02ABEH001020} `

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This publication is cited in the following articles:
1. John L. Lewis, “On a conditional theorem of Littlewood for quasiregular entire functions”, J Anal Math, 62:1 (1994), 169
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