Abstract
A milestone in the evolution of value distribution theory was Ahlfors’ [11] discovery that the main theorems are not based on the analyticity of the mapping functions but can, in essence, be derived from purely metric-topological properties of covering surfaces. We begin the present chapter by following rather closely Ahlfors’ original proof arrangement, unsurpassed in elegance by other presentations. The theory culminates in his fundamental inequality, often referred to as the nonintegrated form of the second main theorem on meromorphic functions. We shall also give this inequality and Picard’s theorem as localized by Noshiro [2] to a transcendental singularity of the inverse function.
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© 1966 D. Van Nostrand Company, Inc.
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Sario, L., Noshiro, K. (1966). Riemannian Images. In: Value Distribution Theory. The University Series in Higher Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4615-8126-0_7
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DOI: https://doi.org/10.1007/978-1-4615-8126-0_7
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4615-8128-4
Online ISBN: 978-1-4615-8126-0
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