Abstract
The sine function assumes every complex number as a value; the exponential function omits only the value O. These examples are significant for the value behavior of entire functions. A famous theorem of E. Picard says that every nonconstant entire function omits at most one value. This so-called little Picard theorem is an astonishing generalization of the theorems of Liouville and Casorati-Weierstrass.
Une fonction entière, qui ne devient jamais ni à a ni à b est nécessairement une constante. (An entire function which is never equal to either a or b must be constant.)
— E. Picard, 1879
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Remmert, R. (1998). The Theorems of Bloch, Picard, and Schottky. In: Classical Topics in Complex Function Theory. Graduate Texts in Mathematics, vol 172. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2956-6_10
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