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

A. Erϋmenko; M. L. Sodin

doi:10.1070/IM1988v030n02ABEH001020

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

A. Erϋmenko, M. L. Sodin

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

It is proved that for any entire function of finite nonzero order there is a set in the plane with density zero and such that for any almost all the roots of the equation belong to 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.

Original language	English
Pages (from-to)	395-402
Number of pages	8
Journal	Mathematics of the USSR - Izvestija
Volume	30
Issue number	2
DOIs	https://doi.org/10.1070/IM1988v030n02ABEH001020
State	Published - 30 Apr 1988

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abstract = "It is proved that for any entire function of finite nonzero order there is a set in the plane with density zero and such that for any almost all the roots of the equation belong to 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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Proof of a conditional theorem of littlewood on the distribution of values of entire functions

Abstract

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