Accession Number : AD0433881


Title :   ON SUMS OF POWERS OF COMPLEX NUMBERS; AN IMPROVED ESTIMATE,


Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER


Personal Author(s) : Atkinson,F. V.


Report Date : DEC 1963


Pagination or Media Count : 32


Abstract : Given n complex numbers, of which at least one has modulus not less than unity, it is shown that for at least one k, where k is less than or equal to n and more than or equal to 1, the sum of the k-th powers of these numbers exceeds 1/3. This improves on earlier estimates of 1/6, or 1/5 for n greater than 8 pi. The problem has an application to the numerical solution of algebraic equations. (Author)


Descriptors :   (*COMPLEX NUMBERS, ALGEBRA), EQUATIONS, NUMERICAL ANALYSIS


Distribution Statement : APPROVED FOR PUBLIC RELEASE