Accession Number:

AD0255904

Title:

MEROMORPHIC FUNCTIONS WITH SECTORS FREE OF ZEROS AND POLES

Descriptive Note:

Corporate Author:

SYRACUSE UNIV N Y

Personal Author(s):

Report Date:

1961-01-01

Pagination or Media Count:

1.0

Abstract:

Let fz be a meromorphic function which is not a polynomial. Assume that all the zeros and poles of f lie on the real axis. Let 0 be given and denote by n r,k the number of zeros of fe U., N. Y. MEROMORPHIC FUNCTIONS WITH SECTORS FREE OF ZEROS AND POLES, by Simon Hellerstein. Jan 61, 15p. Contract AF 49638571 AFOSR-222Unclassified report DESCRIPTORS Mathematics, Functions. Let fz be a meromorphic function which is not a polynomial. Assume that all the zeros and poles of f lie on the real axis. Let 0 be given and denote by n r,k the number of zeros of fkz taking multiplicities into account which lie in the disk z r and outside the angles - arg z - arg z . Then for functions of finite order and r sufficiently large, n r,k K r, where K depends only on f and k. For functions of infinite order n r,k K r2log r log2Tr,f, provided r avoids the values of an exceptional set of finite measure, Tr,f is the Nevanlinna characteristic of f. The theorem is a consequence of a more general one for meromorphic functions with one sector S free of zeros and poles. Here again it is possible to prove that a sector interior to S contains few zeros of the successive derivatives of f. Author

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Distribution Statement:

APPROVED FOR PUBLIC RELEASE