Eisenstein congruences for split reductive groups

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.

Version 2: Minor revision. Accepted for publication in Selecta Mathematica. 38 pages

References in corpus (1)

• Eisenstein congruences for SO(4,3), SO(4,4), spinor and triple product L-values

Cited by in corpus (2)

• Exploring modular forms and the cohomology of local systems on moduli spaces by counting points
• Generic level $p$ Eisenstein congrunces for GSp${}_4$