Vol. 11, No. 4, 2018

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 3, 363–530
Issue 2, 183–362
Issue 1, 1–182

Volume 16, 5 issues

Volume 15, 5 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 8 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN (electronic): 1944-4184
ISSN (print): 1944-4176
 
Author index
To appear
 
Other MSP journals
Locating trinomial zeros

Russell Howell and David Kyle

Vol. 11 (2018), No. 4, 711–720
Abstract

We derive formulas for the number of interior roots (i.e., zeros with modulus less than 1) and exterior roots (i.e., zeros with modulus greater than 1) for trinomials of the form zn + zk 1, where 1 k n 1. Combined with earlier work by Brilleslyper and Schaubroeck, who focus on unimodular roots (i.e., zeros that lie on the unit circle), we give a complete count of the location of zeros of these trinomials.

Keywords
trinomials, complex analysis, Diophantine equations, zeros of functions
Mathematical Subject Classification 2010
Primary: 30C15, 97I80
Secondary: 11-02
Milestones
Received: 21 July 2017
Accepted: 29 August 2017
Published: 15 January 2018

Communicated by Michael Dorff
Authors
Russell Howell
Department of Mathematics
Westmont College
Santa Barbara, CA
United States
David Kyle
Department of Mathematics
Westmont College
Santa Barbara, CA
United States