QUASI-PULLBACK OF CERTAIN SIEGEL MODULAR FORMS AND BORCHERDS PRODUCTS (Automorphic forms, Automorphic representations, Galois representations, and its related topics)

Abstract

A holomorphic torsion invariant of K3 surfaces with involution was introduced by the author [Yoshikawa, K.-I. K3 surfaces with involution, equivariant analytic torsion, and automorphic forms on the moduli space, Invent. Math. 156 (2004), 53-117.], and it has been proved in [Ma, S., Yoshikawa, K.-I. K3 surfaces with involution, equivariant analytic torsion, and automorphic forms on the moduli space IV: The structure of the invariant, Compositio Math. 156 (2020), 1965-2019.] that this invariant is expressed as the product of an explicit Borcherds product and an explicit Siegel modular form. In this note, we report that these automorphic forms are closed under the operation called quasi-pullback (Theorem 5.9). As a result, we obtain some Borcherds products as the quasi-pullback of certain Siegel modular form (Theorem 5.8).