Selecta Mathematica

, Volume 22, Issue 3, pp 1073–1115 | Cite as

Eisenstein congruences for split reductive groups

Article

Abstract

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.

Keywords

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

Mathematics Subject Classification

11F33 11F46 11F67 11F75 

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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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