Vol. 11, No. 4, 2018

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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.

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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