Selecta Mathematica

, Volume 22, Issue 3, pp 1073–1115

Eisenstein congruences for split reductive groups


DOI: 10.1007/s00029-015-0211-0

Cite this article as:
Bergström, J. & Dummigan, N. Sel. Math. New Ser. (2016) 22: 1073. doi:10.1007/s00029-015-0211-0


We present a general conjecture on congruences between Hecke eigenvalues of parabolically induced and cuspidal automorphic representations of split reductive groups, modulo divisors of critical values of certain L-functions. We examine the consequences in several special cases and use the Bloch–Kato conjecture to further motivate a belief in the congruences.


Congruences of modular forms Harder’s conjecture Bloch–Kato conjecture 

Mathematics Subject Classification

11F33 11F46 11F67 11F75 

Copyright information

© Springer International Publishing 2015

Authors and Affiliations

  1. 1.Matematiska institutionenStockholms universitetStockholmSweden
  2. 2.School of Mathematics and StatisticsUniversity of SheffieldSheffieldUK

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