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Schottky's theorem : ウィキペディア英語版
Schottky's theorem
In mathematical complex analysis, Schottky's theorem, introduced by is a quantitative version of Picard's theorem which states that the size |''f''(''z'')| of a holomorphic function ''f'' in the open unit disk that does not take the values 0 or 1 can be bounded in terms of ''z'' and ''f''(0).
Schottky's original theorem did not give an explicit bound for ''f''. gave some weak explicit bounds. gave a strong explicit bound, showing that if ''f'' is holomorphic in the open unit disk and does not take the values 0 or 1 then
:\log |f(z)| \le \frac(7+\max(0,\log |f(0)|)).
Several authors, such as , have given variations of Ahlfors's bound with better constants: in particular gave some bounds whose constants are in some sense the best possible.
==References==

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抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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