RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Sb. (N.S.), 1979, Volume 109(151), Number 4(8), Pages 555–581 (Mi msb2401)  

This article is cited in 3 scientific papers (total in 3 papers)

On asymptotic curves of entire functions of finite order

A. A. Gol'dberg, A. È. Eremenko


Abstract: For any $\rho$, $ 0\leqslant\rho\leqslant\infty$, there exists an entire function of order $\rho$ such that for any asymptotic curve $\Gamma$ on which $f\to\infty$ the relation $l(r,\Gamma)=O(r)$, $r\to\infty$, does not hold, where $l(r,\Gamma)$ is the length of that part of $\Gamma$ contained in the disc $ż:|z|\leqslant r\}$. The same is true of asymptotic curves on which $f\to a\ne\infty$ under the natural restriction that $1/2\leqslant\rho\leqslant\infty$. This disproves a well-known conjecture of Hayman and Erdösh. Several closely related results are obtained.
Bibliography: 24 titles.

Full text: PDF file (2305 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1980, 37:4, 509–533

Bibliographic databases:

UDC: 517.535.4
MSC: 30D15
Received: 20.09.1977

Citation: A. A. Gol'dberg, A. È. Eremenko, “On asymptotic curves of entire functions of finite order”, Mat. Sb. (N.S.), 109(151):4(8) (1979), 555–581; Math. USSR-Sb., 37:4 (1980), 509–533

Citation in format AMSBIB
\Bibitem{GolEre79}
\by A.~A.~Gol'dberg, A.~\`E.~Eremenko
\paper On asymptotic curves of entire functions of finite order
\jour Mat. Sb. (N.S.)
\yr 1979
\vol 109(151)
\issue 4(8)
\pages 555--581
\mathnet{http://mi.mathnet.ru/msb2401}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=545054}
\zmath{https://zbmath.org/?q=an:0443.30037|0416.30022}
\transl
\jour Math. USSR-Sb.
\yr 1980
\vol 37
\issue 4
\pages 509--533
\crossref{https://doi.org/10.1070/SM1980v037n04ABEH001989}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1980LA35500003}


Linking options:
  • http://mi.mathnet.ru/eng/msb2401
  • http://mi.mathnet.ru/eng/msb/v151/i4/p555

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Schleicher D., “Dynamics of Entire Functions”, Holomorphic Dynamical Systems, Lect. Notes Math., 1998, eds. Gentili G., Guenot J., Patrizio G., Springer-Verlag Berlin, 2010, 295–339  crossref  mathscinet  isi
    2. Rottenfusser G., Rueckert J., Rempe L., Schleicher D., “Dynamic Rays of Bounded-Type Entire Functions”, Ann. Math., 173:1 (2011), 77–125  crossref  mathscinet  zmath  isi
    3. Shahverdian A.Yu., “Fine Topology and Estimates for Potentials and Subharmonic Functions”, Comput. Methods Funct. Theory, 11:1 (2011), 71–121  crossref  mathscinet  zmath  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:221
    Full text:65
    References:30
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019