In a paper published in 2004, I introduced a holomorphic torsion invariant for K3 surfaces with involution. This invariant is viewed as a function on the moduli space, which is a modular variety of orthogonal type. In the talk, I will explain the construction of the invariant and its structure as an automorphic function on the moduli space. It is expressed as a product of an explicit Borcherds
product and a Siegel modular form.