ON SUMS OF POWERS OF COMPLEX NUMBERS; AN IMPROVED ESTIMATE,
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1963
- Accession Number
- AD0433881
Entities
People
- F. V. Atkinson
Organizations
- University of Wisconsin–Madison