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Primeable entire functions

Published online by Cambridge University Press:  22 January 2016

Fred Gross ,
Chung-Chun Yang  and
Charles Osgood
Fred Gross
Affiliation:
Mathematics Research Center, Naval Research Laboratory, and University of Maryland, Baltimore County.
Chung-Chun Yang
Affiliation:
Mathematics Research Center, Naval Research Laboratory.
Charles Osgood
Affiliation:
Mathematics Research Center, Naval Research Laboratory.
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An entire function F(z) = f(g(z)) is said to have f(z) and g(z) as left and right factors respe2tively, provided that f(z) is meromorphic and g(z) is entire (g may be meromorphic when f is rational). F(z) is said to be prime (pseudo-prime) if every factorization of the above form implies that one of the functions f and g is bilinear (a rational function). F 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 and g is linear (a polynomial). We recall here that an entire non-periodic function f is prime if and only if it is E-prime [5]. This fact will be useful in the sequel.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 51 , September 1973 , pp. 123 - 130
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1973

References

[1] Baker, I. N., “The value distribution of composite entire functions”, Acta Math. Szeged, Tom 32, (1971).Google Scholar
[2] Borei, E., “Sur les zéros des fonctions entières”, Acta Math., 20, (1897) 357–396.Google Scholar
[3] Edrei, A., “Meromorphic functions with three radically distributed values”, Trans. Amer. Math. Soc., 78, (1955) 271–293.CrossRefGoogle Scholar
[4] Goldstein, R., “On factorization of certain entire functions”, J. Lond. Math. Soc., (2), (1970) pp. 221–224.CrossRefGoogle Scholar
[5] Gross, F., “Factorization of entire functions which are periodic mod g”, Indian J. of pure and applied Math., Vol.2, No.3, (1971).Google Scholar
[6] Gross, F. and Yang, C. C., “The fix-points and factorization of meromorphic functions”, Trans. Amer. Math. Soc., Vol.168, (1972).Google Scholar