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Mat. Zametki, 1969, Volume 6, Issue 4, Pages 437–441 (Mi mz6950)  

Fatou's example

A. Sadullaev

M. V. Lomonosov Moscow State University

Abstract: Examples due to P. Fatou and L. Biberbach show that Picard's little theorem cannot be extended to apply to holomorphic mappings of the complex space $C^n$, $n>1$. These examples are used to construct a pair of functionally independent entire functions of two complex variables such that the image of $C^2$ by the mapping realized by this pair does not contain any sphere. Here we give an example of the same type which implies a stronger assertion concerning the set of values not taken.

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English version:
Mathematical Notes, 1969, 6:4, 717–719

Bibliographic databases:

UDC: 517.5
Received: 10.01.1969

Citation: A. Sadullaev, “Fatou's example”, Mat. Zametki, 6:4 (1969), 437–441; Math. Notes, 6:4 (1969), 717–719

Citation in format AMSBIB
\Bibitem{Sad69}
\by A.~Sadullaev
\paper Fatou's example
\jour Mat. Zametki
\yr 1969
\vol 6
\issue 4
\pages 437--441
\mathnet{http://mi.mathnet.ru/mz6950}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=414944}
\zmath{https://zbmath.org/?q=an:0202.36501|0199.13601}
\transl
\jour Math. Notes
\yr 1969
\vol 6
\issue 4
\pages 717--719
\crossref{https://doi.org/10.1007/BF01093808}


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