On K3 modular functions. (Japanese) Zbl 0619.14024
The author explains his ideas in order to obtain generalized modular functions of several variables. It is expected that, if one has a good family of K3-surfaces over a parameter \(space\quad T,\) one can proceed similarly as in the classical case of elliptic curves. For example, the periods are to satisfy differential equations of hyper-geometric type, the period mapping is to be a mapping into a domain D with \(\dim (D)=\dim (T)\), and the inverse of it is to be expressed explicitly by automorphic functions and forms on D with respect to the monodromy action. The author exhibits several examples of such families to which his method applies. Every K3-surface in these examples admits an elliptic fibration with a holomorphic section. Proofs are found in the author’s other papers.
Reviewer: T.Fujita
MSC:
14J15 | Moduli, classification: analytic theory; relations with modular forms |
11F67 | Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols |
32N99 | Automorphic functions |
14J28 | \(K3\) surfaces and Enriques surfaces |
32J15 | Compact complex surfaces |
32G20 | Period matrices, variation of Hodge structure; degenerations |
11F27 | Theta series; Weil representation; theta correspondences |