# Hokkaido Mathematical Journal

## Hokkaido Mathematical Journal, 36 (2007) pp.143-173

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### Abstract

We represent the $105$ automorphic forms on the $5$-dimensional complex ball $\mathbb B^5$ constructed by Matsumoto-Terasoma as the products of four linear combinations of the pull backs of theta constants under an embedding of $\mathbb B^5$ into the Siegel upper half space of degree $6$. They were used to describe the inverse of the period map for the family of the $4$-fold coverings of the complex projective line branching at eight points.

MSC(Primary) 32N15 11F55, 14J15 automorphic forms, theta constants