## Hokkaido Mathematical Journal

- Hokkaido Math. J.
- Volume 36, Number 1 (2007), 143-173.

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

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

#### 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.

#### Article information

**Source**

Hokkaido Math. J., Volume 36, Number 1 (2007), 143-173.

**Dates**

First available in Project Euclid: 29 September 2010

**Permanent link to this document**

https://projecteuclid.org/euclid.hokmj/1285766656

**Digital Object Identifier**

doi:10.14492/hokmj/1285766656

**Mathematical Reviews number (MathSciNet)**

MR2309827

**Zentralblatt MATH identifier**

1135.11023

**Subjects**

Primary: 32N15: Automorphic functions in symmetric domains

Secondary: 11F55: Other groups and their modular and automorphic forms (several variables) 14J15: Moduli, classification: analytic theory; relations with modular forms [See also 32G13]

**Keywords**

automorphic forms theta constants

#### Citation

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 Math. J. 36 (2007), no. 1, 143--173. doi:10.14492/hokmj/1285766656. https://projecteuclid.org/euclid.hokmj/1285766656