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(

Abstract

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.