Vol. 17, No. 1, 1966

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 332: 1
Vol. 331: 1  2
Vol. 330: 1  2
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Online Archive
Volume:
Issue:
     
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Officers
 
Subscriptions
 
ISSN 1945-5844 (electronic)
ISSN 0030-8730 (print)
 
Special Issues
Author index
To appear
 
Other MSP journals
A certain class of polynomials

Ruth Goodman

Vol. 17 (1966), No. 1, 57–69
Abstract

In generalizing Grace’s Theorem on apolar polynomials, it was convenient (see reference 1) to use a set of relations among the coefficients of a pair of polynomials which is invariant under nonsingular linear transformations of the polynomials. Other invariant relations among their coefficients will define other classes of pairs of polynomials. The present paper establishes a set of relations which is both necessary and sufficient to guarantee that two polynomials of degree n either have a common zero of multiplicity at least n 1 or have their zeros all lying on one circle and so related that if the zeros of one polynomial are transformed, by a linear transformation, into the n-th roots of +1 then the zeros of the other are carried, by the same transformation, into the n-th roots of 1.

Mathematical Subject Classification
Primary: 30.10
Milestones
Received: 8 August 1964
Revised: 8 November 1964
Published: 1 April 1966
Authors
Ruth Goodman