  The aim of this paper is to study algebraic K3 surfaces (defined over the
complex number field) with a symplectic automorphism of prime order. In
particular we consider the action of the automorphism on the second cohomology
with integer coefficients. We determine the invariant sublattice and its
perpendicular complement, and show that the latter coincides with the
Coxeter-Todd lattice in the case of automorphism of order three. We also
compute many explicit examples, with particular attention to elliptic
fibrations.
