Eisenstein congruences for split reductive groups

Research paper by Jonas Bergström, Neil Dummigan

Indexed on: 14 Oct '15Published on: 14 Oct '15Published in: Mathematics - Number Theory


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.