The order of entire functions with radially distributed zeros

Abi-Khuzam, Faruk F.

doi:10.1090/S0002-9939-1981-0603604-4

The order of entire functions with radially distributed zeros
HTML articles powered by AMS MathViewer

by Faruk F. Abi-Khuzam PDF

Proc. Amer. Math. Soc. 82 (1981), 71-75 Request permission

Abstract:

It is shown that an entire function with radially distributed zeros has finite order $\lambda$ if it has finite lower order $\mu$. It is then shown that functions with real negative zeros only are extremal for the problem of maximizing the Nevanlinna characteristic in the class of entire functions satisfying $\lambda - \mu > 1$.

References

Albert Edrei, Wolfgang H. J. Fuchs, and Simon Hellerstein, Radial distribution and deficiencies of the values of a meromorphic function, Pacific J. Math. 11 (1961), 135–151. MR 122999
Albert Edrei and Wolfgang H. J. Fuchs, On the growth of meromorphic functions with several deficient values, Trans. Amer. Math. Soc. 93 (1959), 292–328. MR 109887, DOI 10.1090/S0002-9947-1959-0109887-4
Albert Edrei and Wolfgang H. J. Fuchs, Valeurs déficientes et valeurs asymptotiques des fonctions méromorphes, Comment. Math. Helv. 33 (1959), 258–295 (French). MR 123716, DOI 10.1007/BF02565920
W. K. Hayman, Meromorphic functions, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1964. MR 0164038
Joseph Miles and Daniel F. Shea, An extremal problem in value-distribution theory, Quart. J. Math. Oxford Ser. (2) 24 (1973), 377–383. MR 324041, DOI 10.1093/qmath/24.1.377
D. F. Shea, On the Valiron deficiencies of meromorphic functions of finite order, Trans. Amer. Math. Soc. 124 (1966), 201–227. MR 200458, DOI 10.1090/S0002-9947-1966-0200458-1

Über die Gleichverteilung von Zahlen

7

J. M. Whittaker, Entire functions of irregular growth take every value, Bull. London Math. Soc. 4 (1972), 130–132. MR 318482, DOI 10.1112/blms/4.2.130