An improved version of the big Picard theorem for polyanalytic functions

1. M. B. Balk and M. F. Zuev, “On polyanalytic functions,” Usp. Matem. Nauk,25, No. 5, 203–226 (1970).

   Google Scholar 

2. M. B. Balk, “On values taken by entire polyanalytic functions,” Dokl. Akad. Nauk SSSR,167, No. 2, 12–15 (1966).

   Google Scholar 

3. W. Bosch and P. Krajkiewicz, “The big Picard theorem for polyanalytic functions,” Proc. Amer. Math. Soc.,26, No. 1, 145–150 (1970).

   Google Scholar 

4. H. L. Selberg, “Über die Wertverteilung der algebroiden Funktionen,” Mat. Z.,31, No. 5, 709–728 (1930).

   Google Scholar 

5. S. Stoilow, Lectures on the Topological Principles of the Theory of Analytic Functions [Russian translation], Nauka, Moscow (1964), p. 226.

   Google Scholar 

6. M. B. Balk and M. F. Zuev, “On the number of values taken by an entire polyanalytic function in a nonisolated fashion,” Izv. Akad. Nauk ArmSSR, Matematika,7, No. 5, 313–324 (1972).

   Google Scholar 

7. T. Kuroda, “A property of some open Riemann surfaces and its application,” Nagoya Math. J.,6, 77–84 (1953).

   Google Scholar 

8. Z. Kuramochi, “On a covering property of abstract Riemann surfaces,” Osaka Math. J.,6, 93–103 (1954).

   Google Scholar 

9. T. Kuroda, “On analytic functions on some Riemann surfaces,” Nagoya Math. J.,10, 27–50 (1956).

   Google Scholar 

10. A. Mori, “On Riemann surfaces on which no bounded harmonic function exists,” J. Math. Soc. Japan,3, 247–257 (1951).

    Google Scholar 

11. L. Sario and K. Noshiro, Value Distribution, Van Nostrand, New York (1966).

    Google Scholar 

12. G. Rémoundos, Extension aux fonctions algébroides multiformes du théorème de M. Picard et de ses généralisations (Mem. Sci. Math., Fasc. 23), Gauthier-Villars, Paris (1927).

    Google Scholar 

13. P. Krajkiewicz, “Polyanalytic functions with exceptional values,” Trans. Amer. Math. Soc.,197, 181–210 (1974).

    Google Scholar 

14. M. B. Balk, “On factorization of a polyanalytic function in the neighborhood of an isolated singularity,” Izv. Akad. Nauk ArmSSR, Matematika,10, No. 5, 389–397 (1975).

    Google Scholar 

Download references