Theorems in complex analysis

Schottky's theorem

In mathematical complex analysis, Schottky's theorem, introduced by Schottky is a quantitative version of Picard's theorem. It states that for a holomorphic function f in the open unit disk that does not take the values 0 or 1, the value of |f(z)| can be bounded in terms of z and f(0). Schottky's original theorem did not give an explicit bound for f. Ostrowski gave some weak explicit bounds. , theorem B) 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 . 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. (Wikipedia).

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Related pages

Complex analysis | Holomorphic function