  Let X be a complex projective K3 surface, and let T(X) be its transcendental
lattice; the characteristic polynomials of the isometries of T(X) induced by
automorphisms of X are powers of cyclotomic polynomials. Which powers of
cyclotomic polynomials occur ? The aim of this note is to answer this question,
as well as related ones, and give an alternative approach to some results of
Kondo, Machida, Oguiso, Vorontsov, Xiao and Zhang; this leads to questions and
results concerning orthogonal groups of lattices.
