In this paper we study the characteristic polynomials (S(x)=\det(xI−F| II_{p,q})) of automorphisms of even unimodular lattices with signature ((p,q)). In particular, we show that any Salem polynomial of degree (2n) satisfying (S(−1)S(1)=(−1)^n) arises from an automorphism of an indefinite lattice, a result with applications to K3 surfaces.
In this paper we show that the cyclotomic factors of the En Coxeter polynomials depend only on the value of (n) mod 360, and come exclusively from spherical subdiagrams.
