On Complex Pisot Numbers That Are Roots of Borwein Trinomials

Paulius Drungilas (), Jonas Jankauskas and Grintas Junevičius
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Paulius Drungilas: Institute of Mathematics, Department of Mathematics and Informatics, Vilnius University, Naugarduko 24, LT-03225 Vilnius, Lithuania
Jonas Jankauskas: Institute of Mathematics, Department of Mathematics and Informatics, Vilnius University, Naugarduko 24, LT-03225 Vilnius, Lithuania
Grintas Junevičius: Institute of Mathematics, Department of Mathematics and Informatics, Vilnius University, Naugarduko 24, LT-03225 Vilnius, Lithuania

Mathematics, 2024, vol. 12, issue 8, 1-10

Abstract: 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.

Keywords: Borwein trinomial; complex Pisot number; unimodular number; root of unity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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