On Complex Pisot Numbers That Are Roots of Borwein Trinomials

Let n> m be positive integers. Polynomials of the form z(n )+/- z(m )+/- 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.