Accession Number:

AD0716559

Title:

A Note on the Tumura-Clunie Theorem (Zamechanie k Teoreme Tumura-Kluni),

Descriptive Note:

Corporate Author:

NAVAL RESEARCH LAB WASHINGTON D C

Personal Author(s):

Report Date:

1970-12-11

Pagination or Media Count:

4.0

Abstract:

In 1937, Tumura expressed the following statement If the entire function fz and f sup kz, k or 2, have no zeros, then fz expaz b however, its proof had important gaps. A strict proof of Tumuras theorem was recently given by Clunie, as reported in a survey by Hayman Clunie also proved the following theorem If fz is meromorphic in z not equal to infinity, and fz and f sup kz, k or 2, have a finite number of zeroes and poles, then fz has finite order rho. In the present note the author proves a statement not contained in Clunies result, but which, with the use of this result, will permit one to give an exact expression for rho within the assumptions of Clunies theorem. Author

Subject Categories:

  • Numerical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE