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Bloch's theorem (complex variables) : ウィキペディア英語版 | Bloch's theorem (complex variables) In complex analysis, a field within mathematics, Bloch's theorem gives a lower bound on the size of a disc in which an inverse to a holomorphic function exists. It is named after André Bloch. ==Statement== Let ''f'' be a holomorphic function in the unit disk |''z''| ≤ 1. Suppose that |''f′''(0)| = 1. Then there exists a disc of radius ''b'' and an analytic function φ in this disc, such that ''f''(φ(''z'')) = ''z'' for all ''z'' in this disc. Here ''b'' > 1/72 is an absolute constant.
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