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arXiv · 2010.00650

On Constant Terms of Eisenstein Series

Samit Dasgupta·Mahesh Kakde
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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.

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Samit Dasgupta, Mahesh Kakde. 2020-10-01. On Constant Terms of Eisenstein Series. https://arxiv.org/abs/2010.00650

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