## On constant terms of Eisenstein series

### Volume 200 / 2021

Acta Arithmetica 200 (2021), 119-147
MSC: Primary 11F41; Secondary 11F30.
DOI: 10.4064/aa200621-24-2
Published online: 6 October 2021

#### Abstract

We calculate the constant terms of certain Hilbert modular Eisenstein series at all cusps. Our formula relates these constant terms to special values of Hecke $L$-series. This builds on previous work of Ozawa, in which a restricted class of Eisenstein series were studied. Our results have direct arithmetic applications—in separate work we apply these formulas to prove the Brumer–Stark conjecture away from $p=2$ and to give an exact analytic formula for Brumer–Stark units.