On Complex Pisot Numbers That Are Roots of Borwein Trinomials

Abstract

Let n>m be positive integers. Polynomials of the form zn±zm±1 are called Borwein trinomials. Using an old result of Bohl, we derive explicit formulas for the number of roots of a Borwein trinomial inside the unit circle |z|1. Based on this, we determine all Borwein trinomials that have a complex Pisot number as a root. There are exactly 29 such trinomials.

Keywords

• Borwein trinomial
• complex Pisot number
• unimodular number
• root of unity