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Mathematics of the USSR-Izvestiya, 1988, Volume 30, Issue 2, Pages 395–402
DOI: https://doi.org/10.1070/IM1988v030n02ABEH001020 (Mi im1302) 		 
This article is cited in 2 scientific papers (total in 2 papers)

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

A. È. Eremenko, M. L. Sodin
English version PDF (387 kB) Citations (2)
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DOI: https://doi.org/10.1070/IM1988v030n02ABEH001020
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.
Bibliography: 11 titles.
Received: 30.01.1985
Russian version:
Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 1987, Volume 51, Issue 2, Pages 421–428
Bibliographic databases:
UDC: 517.53
MSC: Primary 30D35; Secondary 30C10
Language: English
Original paper language: Russian
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/im1302}
\mathscinet{http://mathscinet.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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  • https://www.mathnet.ru/eng/im/v51/i2/p421
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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    Abstract page:378
    Russian version PDF:119
    English version PDF:21
    References:68
    First page:1
     
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