Journal ArticleDOI
Le théorème de Picard-Borel et la théorie des fonctions méromorphes
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This article is published in American Mathematical Monthly.The article was published on 1930-08-01. It has received 289 citations till now.read more
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Value Distribution of Meromorphic Functions
TL;DR: A survey of results after 1970 can be found in this paper, where the authors present a survey of meromorphic functions of finite-order functions with respect to Riemann surfaces.
Journal ArticleDOI
Holomorphic curves with shift-invariant hyperplane preimages
TL;DR: In this article, a difference analogue of M. Green's Picard-type theorem for holomorphic curves is presented, which can be described as a difference analog of Green's first main theorem for the Casorati determinant and an extended version of the difference analogue on the logarithmic derivatives.
Journal ArticleDOI
Value sharing results for shifts of meromorphic functions, and sufficient conditions for periodicity
TL;DR: In this paper, it was shown that if a meromorphic function f (z ) is of finite order and shares two values CM and one value IM with its shift f ( z + c ), then f is a periodic function with period c. The assumption on the order of f can be dropped if f shares two shifts in different directions, leading to a new way of characterizing elliptic functions.
Journal ArticleDOI
Meromorphe Funktionen, die mit ihrer Ableitung Werte teilen
Erwin Mues,Norbert Steinmetz +1 more
TL;DR: In this article, it was shown that the functions f(z)=αez are the only nonconstant entire (meromorphic) functions which share two (three) distinct finite values with their derivative.
Journal ArticleDOI
On a class of conformal metrics.
TL;DR: In this article, the Bloch constant is at least as large as it appeared to me that the resources of the theory of metrics of negative curvature offered rich possibilities from a function-theoretic point of view, and the parallelism between certain properties of subharmonic functions and those of the metrics introduced by Ahlfors [1] is so striking that we are led to ask whether one can introduce a class of metrics including the metrics of Ahelfors for which not only does a Schwarz-Pick-Ahlfors lemma hold, but also requirements of different