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Prime Entire Functions with Prescribed Nevanlinna Deficiency

Published online by Cambridge University Press:  22 January 2016

Fred Gross ,
Charles Osgood  and
Chung-Chun yang
Fred Gross
Affiliation:
Naval Research Laboratory
Charles Osgood
Affiliation:
Naval Research Laboratory
Chung-Chun yang
Affiliation:
Naval Research Laboratory
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According to [4] a meromorphic function h(z) = f(g)(z) is said to have f(z) and g(z) as left and right factors respectively, provided that f(z) is non-linear and meromorphic and g(z) is non-linear and entire (g may be meromorphic when f(z) is rational). h(z) is said to be E-prime (E-pseudo prime) if every factorization of the above form into entire factors implies that one of the functions f, or g is linear (polynomial). h(z) is said to be prime (pseudo-prime) if every factorization of the above form, where the factors may be meromorphic, implies that one of f or g is linear (a polynomial or f is rational).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 47 , September 1972 , pp. 91 - 99
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1972

References

[1] Borel, E., Sur les zeros des fonctions entieres, Acta Math., 20 (1897), p. 387.Google Scholar
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[3] Goldstein, R., On factorisation of certain entire functions, J. Lond. Math. Soc, (2), 2 (1970), pp.221–224.Google Scholar
[4] Gross, F., On factorization of meromorphic functions, Trans. Amer. Math. Soc, Vol. 131, No. 1, 1968.Google Scholar
[5] Gross, F., Factorization of entire functions which are periodic mod g, Indian Journal of Pure nad Applied Mathematics, Vol. 2, No. 3, 1971, p. 568.Google Scholar
[6] Hayman, W. K., Meromorphic functions, Oxford, 1964.Google Scholar
[7] Nevanlinna, R., Le theoreme de Picard-Borel et la theorie des fonctions meromorphes, Paris, Gauthier-Villars, 1929, p. 51.Google Scholar