Geodesic
Proof of a~conditional theorem of Littlewood on the distribution of values of entire functions
Izvestiya. Mathematics , Tome 30 (1988) no. 2, pp. 395-402

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
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     author = {A. \`E. Eremenko and M. L. Sodin},
     title = {Proof of a~conditional theorem of {Littlewood} on the distribution of values of entire functions},
     journal = {Izvestiya. Mathematics },
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     number = {2},
     year = {1988},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1988_30_2_a11/}
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A. È. Eremenko; M. L. Sodin. Proof of a~conditional theorem of Littlewood on the distribution of values of entire functions. Izvestiya. Mathematics , Tome 30 (1988) no. 2, pp. 395-402. http://geodesic.mathdoc.fr/item/IM2_1988_30_2_a11/