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Factorization of meromorphic functions and some open problems

  • Fred Gross
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 599)

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References

  1. 1.
    I. N. Baker, On Some Results of A. Renyi and C. Renyi Concerning Periodic Entire Functions, Acta. Sci. Math. (Szeged) 27 (1966), 197–200.MathSciNetzbMATHGoogle Scholar
  2. 2.
    I. N. Baker and F. Gross, On Factorizing Entire Functions, Proc. Lond. Math. Soc. 18 (1968), 69–76.MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    _____, Further Results on Factorization of Entire Functions, Proc. Symp. in Pure Math. Entire Functions and Related Parts of Analysis 11 (1968), 30–35.MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    P. Erdos and J. Macintyre, Integral Functions with Gap Power Series, Edinburgh Math. Soc. Proc. 10 (1954), 62–70.MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    L. Flatto, A Theorem on Level Curves of Harmonic Functions, J. London Math. Soc. 1 (1969), 470–472.MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    W. H. J. Fuchs and F. Gross, Generalization of a Theorem of A. and C. Renyi on Periodic Functions, Acta. Sci. Math. (Szeged) 32 (1971), 83–86.MathSciNetzbMATHGoogle Scholar
  7. 7.
    R. Goldstein, On Factorization of Certain Entire Functions, J. London. Math. Soc. 2 (1970), 221–224.MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    _____, On Factorization of Certain Entire Functions II, Proc. Lond. Math. Soc. 3 (1971), 267–272.MathSciNetzbMATHGoogle Scholar
  9. 9.
    F. Gross, On Factorization of Elliptic Functions, Canadian J. Math. 20 (1968), 486–494.MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    _____, On Factorization of Meromorphic Functions, Trans. A.M.S. 131 (1968), 215–222.MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    , On the Distribution of Values of Meromorphic Functions, Trans. A.M.S. 131 (1968), 199–214.MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    _____, Prime Entire Functions, Trans. A.M.S. 161 (1971), 219–233.MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    _____, Factorization of Meromorphic Functions, U.S. Gov. Printing Office, 1972.Google Scholar
  14. 14.
    _____, On Factorization Theory for Meromorphic Functions, Comm. Math. Univ. Sancti Pauli, Tokyo 24 (1975), 47–60.MathSciNetzbMATHGoogle Scholar
  15. 15.
    F. Gross, C. Osgood and C. C. Yang, Prime Entire Functions with Prescribed Nevanlinna Deficiency, Nagoya Math. J. 47 (1972), 91–99.MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    _____, On Entire Solutions of a Functional Equation in the Theory of Fluids, J. Math. Phys. 16 (1975), 2142–2147.MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    F. Gross and C. C. Yang, On Factorization of Entire Functions with Infinitely Many Real Zeros, Ind. J. Pure and App. Math. 3 (1972), 1183–1194.MathSciNetzbMATHGoogle Scholar
  18. 18.
    _____, The Fix-points and Factorization of Meromorphic Functions, Trans. A.M.S. 168 (1972), 211–219.MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    _____, Further Results on Prime Entire Functions, Trans. A.M.S. 192 (1974), 347–355.MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    _____, On Pseudo-prime Entire Functions, Tohoku Math. J. 26 (1974), 65–71.MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    G. Halasz, On Periodicity of Composed Integral Functions, Period. Math. Hungar. 2 (1972), 78–83.MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    H. Kneser, Reele Analytische Lösungen der Gleichung ϕ(ϕ(x))=exund Verwandte Funktionalgleichungen, J. Reine Angew. Math. 187 (1950), 56–57.MathSciNetGoogle Scholar
  23. 23.
    E. Mues, Zur Faktorisierung Elliptischer Funktionen, Math. Z. 120 (1971), 157–164.MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    R. Nevanlinna, Le Théorémes de Picard-Borel et la Théorie des Fonctions Méromorphes, Gauthier-Villars, Paris, 1929.zbMATHGoogle Scholar
  25. 25.
    M. Ozawa, On Certain Criteria for the Left-Primeness of Entire Functions, Kodai Math. Sem. Rep. 26 (1975), 304–317.MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    _____, Factorization of Entire Functions, Tohoku Math J. 27 (1975), 321–336.MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    A. K. Pizer, A Problem on Rational Functions, Amer. Math. Monthly 80 (1973), 552–553.MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    G. S. Propkopovič, The Fixed Points of Memomorphic Functions, Ukrain. Mat. Z. 25 (1973), 248–260.MathSciNetGoogle Scholar
  29. 29.
    A. Renyi and C. Renyi, Some Remarks on Periodic Entire Functions, J. Analyse Math. 14 (1965), 303–310.MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    J. F. Ritt, Prime and Composite Polynomials, Trans. A.M.S. 23 (1922), 51–66.MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    P. C. Rosenbloom, The Fix-points of Entire Function, Medd. Lunds. Univ. Mat-Sem. Suppl., Ed. M. Riesz, (1952), 186–192.Google Scholar
  32. 32.
    A. L. Rubel and C. C. Yang, Interpolation and an Avoidable Family of Meromorphic Functions, Mich. Math. J. 20 (1973), 289–296.MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • Fred Gross
    • 1
  1. 1.University of Maryland, Baltimore CountyBaltimore

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