Hokkaido Mathematical Journal

MATSUMOTO K., MINOWA T., NISHIMURA R.,

Automorphic forms on the $5$-dimensional complex ball with respect to the Picard modular group over $\mathbb Z[i]$ .

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
MSC(Secondary)11F55, 14J15
Uncontrolled Keywordsautomorphic forms, theta constants