  This is the abstruct of the revised paper. We study the equivariant analytic
torsion for K3 surfaces with an anti-symplectic involution with the invariant
lattice M (such a surface is called a 2-elementary K3 surface of type M in this
paper), and show that it (together with the analytic torsion of the fixed
curves) can be identified with the automorphic form on the moduli space
characterizing the discriminant locus. Three lattices A_1, II_{1,1}(2),
II_{1,9}(2) are of particular interest, because they consist of the building
blocks of 2-elementary lattices. An explicit formula is given for them. In
particular, if M is twice the Enriques lattice, the automorphic form coincides
with Borcherds's Phi-function which confirms an observation by
Jorgenson-Todorov and Harvey-Moore. Some other examples are shown to be related
to Borcherds's product and generalized Kac-Moody algebras.
