Let ψ be the period map for a family of the cyclic triple coverings of the complex projective line branching at six points. The symmetric group _S_6 acts on this family and on its image under ψ. In this paper, we give an _S_6-equivariant expression of _ψ_−1 in terms of fifteen theta constants.
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Keiji Matsumoto, Theta Constants Associated with the Cyclic Triple Coverings of the Complex Projective Line Branching at Six Points Klein-Gordon equations is studied in the Sobolev space Hs = Hs(. Publ. Res. Inst. Math. Sci. 37 (2001), no. 3, pp. 419–440