Abstract
The origin of the Bloch Principle can seemingly be traced back to Bloch’s dictum, “Nihil est in infinito quod non prius fuerit in finito” found on p. 2 of his 1926 monograph, as well as on p. 84 of [1926b]. It may be translated as: Nothing exists in the infinite plane that has not been previously done in the finite disk. In modern parlance it is the hypothesis that a family of analytic (meromorphic) functions which have a common property р in a domain Ω will in general be a normal family if р reduces an analytic (meromorphic) function in to a constant. The property of omitting two (resp. three) given values of the FNT is one such example. However, the connection between the modern Bloch Principle and Bloch’s original utterance is tenuous at best.KeywordsAnalytic FunctionCompact SubsetMeromorphic FunctionNormal PropertyNormal FamilyThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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