Constant terms of Eisenstein series over a totally real field

Abstract

In this paper we compute constant terms of the Eisenstein series defined over a totally real field at all cusps. We explicitly describe the constant terms of Eisenstein series at each equivalence class of cusps in terms of special values of Hecke [Formula: see text]-functions. This investigation is motivated by M. Ohta’s work on congruence modules related to the Eisenstein series defined over the field of rational numbers.