Automorphisms of even unimodular lattices and unramified Salem numbers

In this paper we study the characteristic polynomials S(x)=det(xI−FIIp,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.