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On constant terms of Eisenstein series

Volume 200 / 2021

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


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.


  • Samit DasguptaDepartment of Mathematics
    Duke University
    Durham, NC 27708-0320, U.S.A.
  • Mahesh KakdeDepartment of Mathematics
    Indian Institute of Science
    Bangalore 560012, India

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