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Математическая физика, анализ, геометрия, 2004, том 11, номер 4, страницы 492–506
(Mi jmag223)
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Coarse equidistribution of the argument of entire functions of finite order
Fëdor Nazarova, Mikhail Sodinb a Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
b School of Mathematics, Tel Aviv University, Tel Aviv, 69978, Israel
Аннотация:
Given a sector $S\subset\mathbb C$ and an entire function $f$ of order $\rho$, we estimate from below the relative area of the preimage $f^{-1}S$. We show that there exist arbitrarily large $r$ such that for any sector $S$ of opening $\alpha$, the relative area of the set $\{f^{-1}S\}\cap r\mathbb D$ is bounded from below by $\alpha\cdot\kappa(\rho)$, where $\kappa(\rho)>0$ depends only on $\rho$, and $\kappa(\rho)\sim\mathrm{const}\,\rho^{-1}$ for $\rho\to\infty$.
Поступила в редакцию: 20.09.2004
Образец цитирования:
Fëdor Nazarov, Mikhail Sodin, “Coarse equidistribution of the argument of entire functions of finite order”, Матем. физ., анал., геом., 11:4 (2004), 492–506
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/jmag223 https://www.mathnet.ru/rus/jmag/v11/i4/p492
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Страница аннотации: | 217 | PDF полного текста: | 72 |
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