Corpus ID: 219556120

On Constant Terms of Eisenstein Series

@article{Dasgupta2020OnCT,
  title={On Constant Terms of Eisenstein Series},
  author={S. Dasgupta and M. Kakde},
  journal={arXiv: Number Theory},
  year={2020}
}
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. 
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