Cyclotomic factors of Coxeter polynomials

Benedict H. Gross, Eriko Hironaka, Curtis T. McMullen

In this paper we determine which roots of unity are zeros of the En Coxeter polynomial. We show that these roots come exclusively from splittings of En into spherical subdiagrams; in particular they have order 2, 3, 5, 8, 12, 18, or 30, and they only depend on the value of n mod 360 (provided we exclude the special case n = 9).