Introduction

Abstract

The Hilbert modular group

$${{\Gamma }_{K}} = SL\left( {2,o} \right)$$

is the group of all 2 × 2 matrices of determinant 1 with coefficients in the ring o of integers of a totally real number field K ⊃ Q. This group and the corresponding spaces and functions — the Hilbert modular varieties and Hilbert modular forms — have been subject of many investigations starting with the Blumenthal papers [6].